No, it isn't true; God is the same from one end of the Bible to the other. His character is unchanging, His love is unchanging, His purity is unchanging -- and His plan for the human race is unchanging. The Bible says, "I the Lord do not change" (Malachi 3:6).
What did change in the Bible was the situation in which God's people found themselves. In the Old Testament, for example, God's people were often surrounded by nations that rejected God and wanted to destroy them. At times, even God's people turned against Him and adopted the immoral ways of their pagan neighbors. God gave them every opportunity to repent, but sometimes He had no choice but to bring judgment upon them. Never forget: God is holy and just, and eventually all the evils of this world will be destroyed (as the New Testament teaches).
But God is also a God of love. In His love He created us, in His love He takes care of us, and in His love He provided the way for our sins to be forgiven so we could be with Him forever. That way is Jesus Christ, whose coming was foretold in the Old Testament and recorded in the New Testament. The Bible says, "The Lord is compassionate and gracious, slow to anger, abounding in love" (Psalm 103:8).
I invite you to discover the Bible for yourself. But most of all, I invite you to discover the One who is at its center -- Jesus Christ -- by giving your life to Him.