This is such a good question and worth checking into because I dare say that there are only a few that believe we can become perfect. But we need to know if this is true or a false belief. Lets check it out.
In the old testament there were men that God called blameless and just.
Genesis 6:8,9 "But Noah found grace in the eyes of the Lord. This the geneology of Noah. Noah was a just man, perfect in his generations. Noah walked with God."
Genesis 17:1 "When Abram was ninety-nine years old, the Lord appeared to Abram and said to him, 'I am Almighty God; walk before Me and be blameless."
Job 1:1 "There was a man in the land of Uz, whose name was Job; and that man was blameless and upright, and one who feared God and shunned evil."
Psalm 18:32 "It is God who arms me with strength, and makes my way perfect."
Psalm 19:7-11 "The law of the Lord is perfect, converting the soul: the testimony of the Lord is sure, making wise the simple. The statutes of the Lord are right, rejoicing the heart: the commandment of the Lord is pure, enlightening the eyes. The fear of the Lord is clean, enduring forever: the judgments of the Lord are true and righteous altogether. More to be desire are they than gold, yea, than much fine gold: sweeter also than honey and the honeycomb. Moreover by them is thy servant warned: and in keeping of them there is great reward."
Psalm 138:8 "The Lord will perfect that which concerns me, Your mercy O lord, endures forever; Do not forsake the work of your hands."
John 17:23 (Jesus prayer for us) "I in them, and You in Me; that they be made perfect in one, that the world may know that You have sent Me, and have loved them as You have loved Me."
2 Corinthians 7:1 "Therefore, having these promises, beloved, let us cleanse ourselves from all filthiness of the flesh and spirit, perfecting holiness in the fear of the Lord."
2 Corinthians 12:9 "And He said to me, 'My grace is sufficient for you, for my strength is made perfect in weakness."
Colossians 1:28 "Him we preach, warning every man in all wisdom, that we may present every man perfect in Christ Jesus."
Colossians 3:14 "But above all these things put on love, which is the bond of perfection."
2 Timothy 3:16,17 "All scripture is given by inspiration of God, and is profitable for doctrine, reproof, correction, for instruction in righteousness, that the man of God may be complete, thoroughly equipped for every good work."
1 Peter 5:10 "But may the God of all grace who called us unto His eternal glory by Christ Jesus, after you have suffered a while, perfect, establish and strengthen and settle you."
1 John 2:5 "Whoever keeps His word, truly the love of God is perfected in Him. By this we know that we are in Him."
Philippians 3:12 (This is Hope) "Not that I have already attained or am already perfected but I press on that I may lay hold of that for which Christ Jesus has also laid hold of me."
I know this is a hard thing to understand, but if we listen closely to what Jesus is telling us in His word, it is as simple as simple can be. The reason it is hard is because we have an aversion to being what God truly wants us to be, because we think in our sinful mind that it is impossible but with God all things are possible. We follow on to know the Lord minute, by minute, day by day and so on until He comes. It is not for us to perfect our characters, it is God's job and He knows how to do it best. It may come through trials, or suffering, but even then isn't it worth everlasting life which can never be taken away from us? Sanctification is the work of a life time. It doesn't happen over night or even in a year or years. We are made perfect day by day as we encounter Him through His word. If we fall which we can easily do if we take our eyes off Him even for a moment, He will pick us up and give us the strength to go on. I want to stress, it is not our work, 'it is God that works in us to will and to do of His good pleasure' so give your life to Him and let Him have complete control and see the difference this makes in your life and mine. It will be entirely new, I can vouch for that. It makes you a new creation in Christ. Grandma Joan