Because God is righteous and just, it is necessary that He also has the attribute of wrath. God’s wrath is an aspect of His righteousness, whereas our anger is often an aspect of our unrighteousness. In God, “wrath” means that He intensely hates all sin.
"For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who suppress the truth in unrighteousness” (Rom 1:18).
a. God’s wrath is emphasized in Scripture.
It may surprise us to find how often the Bible talks about God's wrath and, also, that it is mentioned no less frequently in the New Testament than in the Old Testament. In fact, since God is unchangeable in His nature, He always has to respond to us in the same way. That means that He always has to respond to sin with hatred of that sin, just as He always responds to that which is good and right with pleasure. He is often faced with sin so His response is frequently wrath. The descriptions of God's wrath usually occur in the contexts where God's people sin greatly against Him (e.g., Ex 32:9-10; Deut 9:7-8). The same idea is also frequently found in the New Testament, particularly with regard to the sin of unbelief (e.g., John 3:36; Rom 1:18).
". . . because they did not receive the love of truth so as to be saved, for this reason God will send upon them a deluding influence so that they will believe what is false, in order that they all may be judged who did not believe the truth, but took pleasure in wickedness" (2 Thess 2:10-12).
b. God's wrath should inspire worship.
God's wrath seems to be such a negative concept. But what would God be like if He were a God Who did not hate sin? Since sin is hateful it is worthy of being hated. It is a virtue (not a failure in loving) to hate sin (see Zech 8:17; Heb 1:9). As such, it is an attribute of God that we should seek to imitate. A God who delighted in or ignored something so hateful as sin would not be worthy of worship. But knowing that God will ultimately right all that is wrong leads us to rejoice in the wrath of God, that punishes all wrongdoing and makes way for a new heaven and earth in which there will be no unrighteousness.
c. God's wrath should not cause fear in Christians.
The wonder is that, although "we were by nature children of wrath, like the rest of mankind" (Eph 2:3), we now have trusted Jesus, "Who delivers us from the wrath to come" (1 Thess 1:10). As we think of the wrath that we deserved, but which was poured out on Jesus instead, we worship in amazement.
(Spotlight 8, Lesson 10 in Doctrine 101: Learning about God)