Although the word "purgatory" is not found in Scripture. Scripture points to a place of suffering in the after life:
1 Corinthians 3:10 According to the grace of God which is given unto me, as a wise masterbuilder, I have laid the foundation, and another buildeth thereon. But let every man take heed how he buildeth thereupon. 11 For other foundation can no man lay than that is laid, which is Jesus Christ. 12 Now if any man build upon this foundation gold, silver, precious stones, wood, hay, stubble; 13 Every man's work shall be made manifest: for the day shall declare it, because it shall be revealed by fire; and the fire shall try every man's work of what sort it is. 14 If any man's work abide which he hath built thereupon, he shall receive a reward. 15 If any man's work shall be burned,he shall suffer loss: but he himself shall be saved; yet so as by fire.
And Scripture reveals the existence of a spiritual prison, in the afterlife, where good men go to suffer at the hands of Satan:
Revelation 2:10 Fear none of those things which thou shalt suffer: behold, the devil shall cast some of you into prison, that ye may be tried; and ye shall have tribulation ten days: be thou faithful unto death, and I will give thee a crown of life.
And Scripture also reveals a place where the dead go for 1000 years.
Revelation 20:5 But the rest of the dead lived not again until the thousand years were finished. This is the first resurrection.
And another verse speaks of a place where Jesus preached to spirits in prison.
1 Peter 3:19 By which also he went and preached unto the spirits in prison;
This is what the Catholic Church calls Purgatory.