By using the Kubo formula, the optical conductivity of strained black phosphorene was studied. The anisotropic band dispersion gives rise to an orientation dependent optical conductivity. The energy gap can be tuned by the uniaxial and biaxial strains which can be observed from the interband optical conductivity polarized along the armchair (x) direction. The preferential conducting direction is along the x direction. The dependence of the intraband optical conductivity along the zigzag (y) direction on the Fermi energy and strain exhibits increasing or decreasing monotonously. However, along the x direction this dependence is complicated which originates from the carriers' inverse-direction movements obtained by two types of the nearest phosphorus atom interactions. The modification of the biaxial strain on the energy structure and optical-absorption property is more effective. The imaginary part of the total optical conductivity (Imσ) can be negative around the threshold of the interband optical transition by modifying the chemical potential. Away from this frequency region, Imσ exhibits positive value. It can be used in the application of the surface plasmon propagations in multilayer dielectric structures.