This paper uses the first-principles and the tight-binding methods to study the electronic structures of twisted bilayer graphene for different angles. The band structures and density of states of twisted bilayer graphene in different angles are calculated. Our analysis points out that there is a linear dispersion relation in a twisted bilayer graphene, which is similar to a monolayer graphene, and the Fermi velocity of twisted graphene is lower and lower with reducing angle. Furthermore, gaps appearing at M point of certain angles, in which the width of gap depends on the twist angle, this gap would strengthen the Raman mode intensity of twisted bilayer graphene, as was confirmed by experiment. The comparison of moire patterns and the location of density of states both certify that AB region of moire patterns is the reason of gap at M point.