Is it right for Christians to seek after eternal rewards?
First, we must determine what earns eternal rewards.
The answer to this is wrapped up in the words of Jesus: "But seek ye first the kingdom of God, and his righteousness; and all these things shall be added unto you" (Matt. 6:33).
The "things" that will be added when a Christian seeks to do what the Kingdom of God requires --absolute obedience to all commands found within His Word are blessings this side of Heaven and are rewards for eternity.
Under this prescription found in Matthew 6:33, it is not only okay to desire and seek eternal rewards, but it is commanded of the believer.
Paul the Apostle made no apologies for saying: "I have fought a good fight, I have finished my course, I have kept the faith: Henceforth there is laid up for me a crown of righteousness, which the Lord, the righteous judge, shall give me at that day: and not to me only, but unto all them also that love his appearing" (2 Tim. 4:7-8).
We must make sure our desires are not selfish inward turning, so that it is all about us. We, as God's children, are to seek with all our hearts to do what He put us here to do. Then, our heavenly father will see to it we are blessed beyond our wildest imaginations in His omniscient timing.