No, we don't know what Jesus looked like; neither the accounts of His life in the Gospels or later writings from the early centuries of the Christian era give us any firm information.
Why didn't God provide us with this information? One reason may be because He knew we might become preoccupied with Jesus' appearance, instead of focusing on what is really important about Him. Some people might even have been tempted to make idols that looked like Him and then worship them–which the Bible clearly forbids.
The important thing is not what Jesus looked like, but who He was and what He did for us. He was God in human flesh, sent from Heaven to save us from our sins by His death on the cross. He was perfect and without sin, but in God's love all our sins were placed on Him, and He died in our place. The Bible says, "Christ died for sins once for all, the righteous for the unrighteous, to bring you to God" (1 Peter 3:18).
Do you want to know what God is like? Look at Jesus Christ–not at His physical appearance, but at His sinless life and character. As the Bible says, "No one has ever seen God, but God the only Son, who is at the Father's side, has made him known" (John 1:18). Then respond to His love by giving your life to Him.