God's anger is real
Scripture does not hide God's anger. God responds strongly when people oppress others, worship what is false, shed innocent blood, or persist in rebellion against him. Romans describes God's wrath, meaning his settled and righteous opposition, being revealed against human ungodliness and wrongdoing (Romans 1:18).
This is not a picture of God losing his temper over small mistakes. His anger is bound up with his goodness. If God saw cruelty, betrayal, violence, and exploitation yet felt nothing, that would not be love. His anger shows that evil matters to him and that he will not simply call it good (Psalm 7:11).
For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who hold the truth in unrighteousness;
He is slow to anger
When God revealed his character to Moses on Mount Sinai, he described himself as merciful, gracious, patient, full of goodness and truth, and willing to forgive (Exodus 34:6-7). That description comes after Israel had made and worshipped a golden calf. Even in a serious moment of rebellion, God's mercy was not absent.
God's patience should never be mistaken for indifference. Nahum says he is slow to anger and great in power, while also making clear that he does not excuse persistent wickedness (Nahum 1:2-3). Both truths belong together. God is compassionate, and God is just.
And the Lord passed by before him, and proclaimed, The Lord, The Lord God, merciful and gracious, longsuffering, and abundant in goodness and truth, Keeping mercy for thousands, forgiving iniquity and transgression and sin, and that will by no means clear the guilty; visiting the iniquity of the fathers upon the children, and upon the children's children, unto the third and to the fourth generation.
God's anger is not human rage
Human anger often becomes selfish, harsh, or careless. James warns that human wrath does not produce the righteousness God desires (James 1:20). God's anger is different. He judges with complete knowledge, without spite, and with concern for what is right.
That does not make this an easy subject. People who have been hurt by angry parents, leaders, or churches may understandably struggle with the idea of God's anger. The Bible invites us to look at God's whole character, not to project the worst human behaviour onto him. He is a righteous judge, but he is also near to those whose hearts are broken (Psalm 34:18).
Jesus shows God's justice and love
The clearest place to see God's response to sin is the cross. Paul says that Christ died for us while we were still sinners, demonstrating God's love rather than waiting for us to make ourselves worthy (Romans 5:8). He also connects Christ's death with rescue from wrath (Romans 5:9).
So God's anger is not the final word for anyone who comes to him. God does not delight in the death of wicked people, but calls them to turn from their ways and live (Ezekiel 33:11). If this question feels personal, you can bring your fear, failure, or confusion to God honestly. The Bible's invitation is not to hide from him, but to turn towards the mercy he offers in Christ.
But God commendeth his love toward us, in that, while we were yet sinners, Christ died for us. Much more then, being now justified by his blood, we shall be saved from wrath through him.