The number of atomic layers is an important parameter for wide band tunability of physical properties of black phosphorus. We theoretically investigate the two photon absorption coefficient in monolayer, bilayer, and trilayer black phosphorus and its dependence on the atomic layer number and polarization direction of the incident light based on the 5-hopping parameter continuous approximate model. The results show that the order of magnitude of the two-photon absorption coefficient of black phosphorus in armchair direction is 10 orders of magnitude larger than that in zigzag direction. The two-photon absorption coefficient of black phosphorus increases with the increase of the number of layers and the absorption peak has a red shift. Moreover, the two-photon absorption coefficient changes periodically with the polarization angle of the incident light as a cosine function. And the two-photon absorption coefficients of black phosphorus are the maximum when the polarization direction of the incident light is along the armchair direction, and the absorption coefficients decrease with the increase of the incidence angle. When the polarization direction is consistent with the zigzag direction, the absorption coefficient is smallest. This study provides a reliable theoretical guidance for the use of black phosphorus in photoelectric devices.