If Jesus is God, yes, a Christian should worship Jesus. Deuteronomy 6:13 says, "You shall fear only the LORD your God; and you shall worship Him and swear by His name" (NASB). Jesus quotes this during His temptation in the wilderness described in Luke 4:1–13 and Matthew 4:1–11. Jesus echoed the command of God that God should be worshipped and only God should be worshipped. So the question becomes "Is Jesus God?"
Should a Christian worship Jesus?
When Jesus asked the disciples who they said He was, Peter answered "You are the Christ, the Son of the living God" (Matthew 16:16). Jesus affirmed the truth of Peter's statement when He replied, "Blessed are you, Simon Bar-Jonah! For flesh and blood has not revealed this to you, but my Father who is in heaven." John 5:18 points out that Jesus "was even calling God his own Father, making himself equal with God." Jesus frequently was worshipped, as we see in the visit of the wise men (Matthew 2:11) and after His resurrection (Luke 24:52). He did not reject this worship, but He accepted it as His due. Since He made it clear that He felt that only God was due worship, and He accepted worship, He was claiming by His actions to be God. So by His own words and actions, Jesus affirmed that He is God. Therefore, we should worship Him.
This raises the question of whether a Christian should worship the Holy Spirit. Similar to the question of whether we should worship Jesus, the question boils down to whether the Holy Spirit is God. In the Great Commission (Matthew 28:19–20), Jesus commands His followers to "Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit." The word "name" is singular, indicating that the Father, the Son, and the Holy Spirit are one. In Acts 5:3, Ananias is accused by Peter of lying to the Holy Spirit, and later in the same passage, Ananias is told, "You have not lied to man but to God" (Acts 5:4). So this affirms that the Holy Spirit is God. First Corinthians 3:16 says that Christians are "God's temple," and 1 Corinthians 6:19 says that a Christian is "a temple of the Holy Spirit." In the same letter, then, God and the Holy Spirit are equated. From these and other references, we must conclude that the Holy Spirit is God. Therefore, it is appropriate for a Christian to worship the Holy Spirit.
So our one God is present in three persons: the Father, the Son, and the Holy Spirit. This is the doctrine of the Trinity. It is appropriate to worship all three, and we should be careful to ensure that our worship of one person of the Trinity does not overshadow our worship of any other person of the Trinity. And to fail to worship any member of the Trinity is sin.
Returning to the original question: yes, a Christian should worship Jesus.
Is Jesus Christ God?
Was Jesus worshipped during His earthly ministry?
How can I worship the Lord in spirit and truth (John 4:23-24)? What is true worship?
How should I worship God?
What is Christian worship?
Truth about the Christian Life