To answer this question, we must first consider who God is. The human mind, however, cannot adequately grasp who He is if it were not for the special revelations He has given us. One avenue of revelation is through God’s creation (Psalm 19:1-6). Creation’s complexity, design, and order lead us to acknowledge there is an awesome Being who brought it into existence and maintains it.
Another avenue is through God’s written Word. From Scripture portions, we may ascertain the attributes, or qualities, that are inherent in God, thus giving us a glimpse of His character. One theologian states that His attributes are “His perfections.” Some of them are: His eternality (Psalm 90:2); His immutability, or unchanging quality (James 1:17); His love (1 John 4:8); His omnipotence, or being all powerful, the Almighty One (Revelation 1:8); His omnipresence, or being everywhere present at all times (Psalm 139:7-11); His holiness, absolute purity and separation from evil (Habakkuk 1:13); His righteousness, or justice (Psalm 11:7); and His truth (Titus 1:2).
This is a brief picture of God who manifested Himself in three persons, Father, Son and Holy Spirit, and the attributes, or perfections, are true for each member of the Godhead. Because God is holy, righteous and true, and He can do nothing inconsistent with Himself, we come to the conclusion that God cannot sin. Since holiness, righteousness, and God’s other perfections are who God is, if God were to sin, He would cease to be God. The fact that God is "holy, holy, holy" prevents Him from doing anything that is unholy, i.e. sinful.
We cannot close, however, without realizing the amazing fact that our holy God involved Himself in mankind’s sin. He sent His one and only Son to this earth to die to pay sin’s penalty. “For Christ died for sins once for all, the righteous for the unrighteous, to bring you to God” (1 Peter 3:18). “He Himself bore our sins in His body on the tree, so that we might die to sins and live for righteousness; by His wounds you have been healed” (1 Peter 2:24). “All have sinned and fall short of the glory of God, and are justified freely by His grace through the redemption that came by Christ Jesus. God presented Him as a sacrifice of atonement, through faith in His blood” (Romans 3:23-25).