Originally from here.
Wrath is defined as “the emotional response to perceived wrong and injustice,” often translated as “anger,” “indignation,” “vexation,” or “irritation.” Both humans and God express wrath. But there is vast difference between the wrath of God and the wrath of man. God’s wrath is holy and always justified; man’s is [never holy and] rarely justified.
In the Old Testament, the wrath of God is a divine response to human sin and disobedience. Idolatry was most often the occasion for divine wrath. Psalm 78:56-66 describes Israel’s idolatry. The wrath of God is consistently directed towards those who do not follow His will (Deuteronomy 1:26-46; Joshua 7:1; Psalm 2:1-6). The Old Testament prophets often wrote of a day in the future, the “day of wrath” (Zephaniah 1:14-15). God’s wrath against sin and disobedience is perfectly justified because His plan for mankind is holy and perfect, just as God Himself is holy and perfect. God provided a way to gain divine favor—repentance—which turns God’s wrath away from the sinner. To reject that perfect plan is to reject God’s love, mercy, grace and favor and incur His righteous wrath.
In the New Testament, Jesus’ teachings support the concept of God as a God of wrath who judges sin. The story of the rich man and Lazarus speaks of the judgment of God and serious consequences for the unrepentant sinner (Luke 16:19-31). Jesus said in John 3:36, “Whoever believes in the Son has eternal life, but whoever rejects the Son will not see life, for God’s wrath remains on Him.” The one who believes in the Son will not suffer God’s wrath for his sin, because the Son took God’s wrath when He died in our place on the cross (Romans 5:6-11). Those who do not believe in the Son, who do not receive Him as Savior, will be judged on the day of wrath (Romans 2:5-6).
Conversely, human wrath is warned against in Romans 12:19, Ephesians 4:26, and Colossians 3:8-10. God alone is able to avenge because His vengeance is perfect and holy, whereas man’s wrath is sinful [because it is associated with revenge, meanness, profanity, telling lies about people], opening him up to demonic influence. For the Christian, anger and wrath are inconsistent with our new nature, which is the nature of Christ Himself (2 Corinthians 5:17). To realize freedom from the domination of wrath, the believer needs the Holy Spirit to sanctify and cleanse his heart of feelings of [ungodly, immoral] wrath and anger. Romans 8 shows victory over sin in the life of one who is living in the Spirit (Romans 8:5-8). Philippians 4:4-7 tells us that the mind controlled by the Spirit is filled with peace.
The wrath of God is a fearsome and terrifying thing. Only those who have been covered by the blood of Christ, shed for us on the cross, can be assured that God’s wrath will never fall on them. “Since we have now been justified by His blood, how much more shall we be saved from God’s wrath through Him!” (Romans 5:9).