Electronic band structure, Partial Density of States (PDOS) and optical properties of β-phase 3,4,9,10-perylenetetracarboxylic dianhydride (β-PTCDA) molecular crystal were systematically investigated by first-principles calculations based on Density Functional Theory (DFT). The contribution of different type of atoms electronic states to different electronic levels was analyzed, and the frequency dependent optical functions such as the dielectric function, absorption coefficient, refractive index and energy loss function of β-PTCDA molecular crystal that changed with optical frequency were analyzed and obtained. The results showed that β-PTCDA is a direct narrow band gap semiconductor, and the electron orbit making larger contribution to the Fermi level is the O 2p electronic state and C 2p electronic state that come from the perylene core, which are also the top of valence band; what makes larger contribution to the bottom of the conduction band is also the C 2p and O 2p electronic states, including anhydride C atoms; in the photon energy range of 2 to 10 eV, the strong light absorption and obvious biaxial anisotropy can be observed. In the optical frequency range with the real part of dielectric function ε1(ω)<0, β-PTCDA molecular crystal has an anisotropic conductivity, which is consistent with the energy loss function.