The interlayer twist angle is an important parameter that can tune the physical properties of graphene in a wide wavelength range. In this paper, we employ an effective continuum model to calculate the band structure of twisted bilayer graphene with different twist angles in the presence and absence of vertical electric field. Based on the transition rate of the electron-photon interaction, we calculate and simulate the optical absorption spectra caused by the interband and intraband transitions around the van Hove singularities. The calculation results show that the optical absorption caused by the interband transitions occurs in the wavelength range from visible light to near-infrared while it appears in far-infrared for intraband transitions. The optical absorption coefficient of the intra-band transitions is almost two orders of magnitude larger than that of inter-band transitions. In the absence of an external electric field, as the twist angle increases, the absorption peak of the inter band transition moves from the infrared light band to the visible light band, but the resonant peak position of its intra-band transition does not change. At the same time, the absorption coefficient values corresponding to the above two transitions will increase. When an electric field is applied perpendicular to the twisted bilayer graphene, the symmetry of the initial band structure of bilayer graphene is destroyed, which results in the splitting of the absorption peaks associated the with interband transitions, and the distance between the two splitting peaks increases with the electric field intensity increasing; while the position and amplitude of the absorption peak associated with the intraband transition are completely unaffected by the applied electric field. The theoretical calculation results in this paper can provide the theoretical guidance for further applying twisted graphene to optoelectronic devices such as tunable dual-band filters.