John 1:18 states, that no one has seen God. However, in the Old Testament there are several verses claiming exactly the opposite (Genesis 17:1; 18:1, Exodus 6:3; 24:10; Amos 9:1, etc.). How do you explain this contradiction?

Answer: John 1:17-18: “(17) Because, while the law was given through Moses; grace and truth came through Jesus Christ. (18) No-one has ever seen God. Only the Son, God, who is at the Fathers side, has revealed him.”
John 6:46: “Not that anyone has seen the Father except the one who is from God; He has seen the Father.”
John 7:29: “I know Him, because I am from Him, and He sent me.” 
1 John 4:12: "No one has ever seen God. Yet if we love on another, God remains in us and His love is brought to perfection in us.”

All these references from John the evangelist’s writings in the New Testament refer to Exodus 33:20: Moses on the mountain:
Exodus 33:18-23: “(18) He [Moses] then said, ‘Please show me your glory.’ (19) Yahweh said, ‘I shall make all my goodness pass before you, and before you I shall pronounce the name Yahweh; and I am gracious to those to whom I am gracious and I take pity on those on whom I take pity.’ (20) But my face’ he said, ‘you cannot see, for no human being can see me and survive.’ (21) Then Yahweh said, ‘Here is a place near me. You will stand on the rock, (22) and when my glory passes by, I shall put you in a cleft of the rock and shield you with my hand until I have gone past. (23) Then I shall take my hand away and you will see my back; but my face will not be seen.’”

Commentary on Ex 33:20 : “God’s sanctity is so removed from human unworthiness (see Leviticus 17:1a) that anyone who looks on God (see Exodus 19:21; Leviticus 16:2, Numbers 4:20) or even hears his voice (see Exodus 20:19; Deuteronomy 5:24-26; see also. 18:16) must perish. For this reason Moses (in Exodus 3:6) and Elijah (in 1 Kings 19:13) and even the seraphim (in Isaiah 6:2) cover their faces in his presence. Anyone who remains alive after seeing God is overwhelmed with astonishment and gratitude (see Genesis 32:31; Deuteronomy 5:24), and with awe (see Judges 6:22-23; 13:22; Isaiah 6:5). It is a favour God rarely concedes (see Exodus 24:11); he grants it to Moses his ‘friend’ (see Exodus 33:11; Numbers 12:7-8, Deuteronomy 34:10) and to Elijah (in 1 Kings 19:11 seq.), both of whom were to be witnesses of the New Testament theophany , the transfiguration of Christ (see Matthew 17:3). In the New Testament the ‘glory’ of God (see Exodus 24:16f and 33:18) is manifested in Jesus (John 1:14); 11:40; 2 Corinthians 4:4), who alone has gazed on the Father (see John 1:18; 6:46; 1 John 4:12). No human being can look on God’s face except in heaven (Matthew 5:8; 1 John 3:2; 1 Corinthians 13:12). (From: “The New Jerusalem Bible”. London: Darton, Longman & Todd, 1985, p. 125.)