Before the flood, according to the Bible, many people lived longer than 120 years. In Genesis 6:3 God declares an end to these long life spans.
And the Lord said, "My Spirit will not strive (abide) with man forever, for he is indeed flesh; yet his days shall be one hundred and twenty years." (Genesis 6:3)NKJV
Some scholars suggest that this 120 years was a prophetic time line until the flood took place. However, we see God's decision was made in Genesis 6:3 after Noah turned 500 in Genesis 5:32.
Noah was 600 years old when the floodwaters were on the earth. (Genesis 7:6)NKJV
Taking these passages we can determine that the flood took place within 100 years after God's decision.
So the prophetic interpretation of the Genesis 6:3 is a wrong one.
Below is a translation of the Oldest Hebrew on Genesis 6:3, I have included it to clear up these different views.
And God said, "My Spirit will not contend with man forever, for he is indeed mortal and their days of life will be 120 years." (Genesis 6:3)
So if the prophetic view is wrong, then why were their people who lived longer than 120 years after the flood?
The Bible is full of contradictions, but only on the surface. God does not say that the shortening life span will be immediate. Despite this, many have read Genesis 6:3 and expect that God would have implemented that decision at that time. We read further on into Genesis and notice that people continued to live much longer than 120 years after the flood. Some would see this obvious contradiction in the Bible as a rational to deny that God exists, but our God does not lie.
I have compiled a chronological list of Biblical people who lived longer than 120 years. As you scroll down the list to the point where God states the "120 year rule" notice the gradual decline to the 120 years of Moses. It is interesting to see that the last recorded person to live beyond 120 years was Jacob (otherwise known as Israel). Jacob was the father of Israel.
Adam = 930 years
Seth = 912 years
Enosh = 905 years
Cainan = 910 years
Mahalalel = 895 years
Jared = 962 years
Enoch =365 years
Methuselah = 969 years
Lamech = 777 years
Noah = 950 years
God says man will only live 120 years
Shem = 600 years
Arphaxad = 438 years
Salah = 433 years
Eber = 464 years
Peleg = 239 years
Reu = 239 years
Serug = 230 years
Nahor = 148 years
Terah = 205 years
Abraham = 175 years
Ishmael = 137 years
Isaac = 180 years
Jacob (Israel) = 147 years
Joseph = 110 years
Moses = 120 years
Joshua = 110 years
You will not find another person in the Bible from this point on that exceeds 120 years.
What God is saying is that the long life span He allowed us to have, created too much evil and wickedness. By shortening the span to 120 years He was also helping man to reduce the evil we individuals are capable of over long periods of time.