Moses was a mediator for the covenant between God and the Hebrews.
Now when all the people perceived the thunderings and the lightnings and the sound of the trumpet and the mountain smoking, the people were afraid and trembled; and they stood afar off, and said to Moses, "You speak to us, and we will hear; but let not God speak to us, lest we die." (Exodus 20:18-19)Moses mediated the covenant, going up and down the mountain at least five times, bringing Gods proposal to the people and the people's response to God. If you look in your Bible, it might even have the heading "Moses Accepted as Mediator" before this section of Scripture. Don't ever let anyone tell you that there is one mediator between God and man.
Jesus is the new Moses. Jesus mediates a new covenant.
Therefore he is the mediator of a new covenant, (Hebrews 9:15)The old covenant was imperfect, and the man Moses was an imperfect mediator. Jesus is the perfect mediator between God and man because Jesus alone is both God and man.
and to Jesus, the mediator of a new covenant, (Hebrews 12:24)
For there is one God, and there is one mediator between God and men, the man Christ Jesus, (1 Timothy 2:5)Jesus is God. Jesus is man. Jesus is therefor the perfect mediator of the new perfect covenant between God and mankind. His mediation is perfect because he is both God and man.