Yes, God is a God of love–and the greatest proof of His love is that He was willing to send His Son into the world to die for our salvation. The Bible says, "This is love: not that we loved God, but that he loved us and sent his Son as an atoning sacrifice for our sins" (1 John 4:10).
You see, only one thing separates us from God, and that is our sin. But sin is far more serious than we usually realize. Sin isn't just something that is a little bit wrong–it is active rebellion against the One who created us. When we sin, we are rejecting God and all He should mean to us. In addition, God is absolutely holy and pure, and we cannot stand in His presence as long as we are stained by our sins.
But God still loves us and He yearns for us to come back to Him and know Him. The only way that could be accomplished was for someone to pay the penalty for our sins–and that "someone" was Christ. He took the judgment and death we deserve by taking our place when He died on the cross for us.
Yes, Christ endured the agony of the cross for you and for me because He loves us. I urge you to respond to His love by asking Him to come into your life today.