In the Book of Exodus, Moses has a conversation with God, and he asks God to show him his glory. And in Exodus 34:5-7, this is what happens:

Then the LORD came down in the cloud and stood there with him and proclaimed his name, the LORD. ⁶ And he passed in front of Moses, proclaiming, "The LORD, the LORD, the compassionate and gracious God, slow to anger, abounding in love and faithfulness, ⁷ maintaining love to thousands, and forgiving wickedness, rebellion and sin. Yet he does not leave the guilty unpunished; he punishes the children and their children for the sin of the fathers to the third and fourth generation."

The Biblical ideal, as demonstrated in the very name and character of God, is not someone who has no anger, but someone who is slow to anger. There is no getting around the fact that God is an angry God; the prophetical books especially are filled with references to God’s anger and wrath – but not a God with out of control, reckless anger, but a God who is slow to anger:

Nahum 1:2-3 The LORD is a jealous and avenging God; the LORD takes vengeance and is filled with wrath. The LORD takes vengeance on his foes and maintains his wrath against his enemies. ³ The LORD is slow to anger and great in power; the LORD will not leave the guilty unpunished.

Zechariah 10:2-3 Therefore the people wander like sheep oppressed for lack of a shepherd. ³ "My anger burns against the shepherds, and I will punish the leaders; for the LORD Almighty will care for his flock, the house of Judah, and make them like a proud horse in battle.

And lest you think this is just some Old Testament God thing, consider Jesus’ anger as well. The words describing Jesus’ emotions are incredibly powerful. He displayed incredible anger at the religious leaders of his day:

Mark 3:1-5 Another time he went into the synagogue, and a man with a shriveled hand was there. ² Some of them were looking for a reason to accuse Jesus, so they watched him closely to see if he would heal him on the Sabbath. ³ Jesus said to the man with the shriveled hand, "Stand up in front of everyone." ⁴ Then Jesus asked them, "Which is lawful on the Sabbath: to do good or to do evil, to save life or to kill?" But they remained silent. ⁵ He looked around at them in anger and, deeply distressed at their stubborn hearts, said to the man, "Stretch out your hand." He stretched it out, and his hand was completely restored.

He had many harsh words for the religious leaders of His day:

Matthew 23:33 "You snakes! You brood of vipers! How will you escape being condemned to hell?

And of course, the most famous display of his anger:

Matthew 21:12-13 Jesus entered the temple area and drove out all who were buying and selling there. He overturned the tables of the money changers and the benches of those selling doves. ¹³ "It is written," he said to them, "'My house will be called a house of prayer,' but you are making it a 'den of robbers.'"

When Jesus came into the temple and found that they had turned the court of the Gentiles into a marketplace for buying sacrifices, he acted in his righteous anger and drove them out. Again, the Biblical ideal is not someone with no anger, for even the Father and Jesus were angry, but someone who is slow to anger.

Proverbs 16:32 puts it this way in the NRSV: One who is slow to anger is better than the mighty, and one whose temper is controlled than one who captures a city.

And in the New Testament:

James 1:19-20 My dear brothers, take note of this: Everyone should be quick to listen, slow to speak and slow to become angry, ²⁰ for man's anger does not bring about the righteous life that God desires.

This, therefore, is the NT ideal:

Ephesians 4:25-27 Therefore each of you must put off falsehood and speak truthfully to his neighbor, for we are all members of one body. ²⁶ "In your anger do not sin": Do not let the sun go down while you are still angry, ²⁷ and do not give the devil a foothold.

Be angry but do not sin.