A recently discovered two-dimensional (2D) layered material phosphorene has attracted considerable interest as a promising p-type semiconducting material. In this work, thermal conductivity ([small kappa]) of monolayer phosphorene is calculated using large-scale classical non-equilibrium molecular dynamics (NEMD) simulations. The predicted thermal conductivities for infinite length armchair and zigzag phosphorene sheets are 63.6+3.9-3.9 and 110.7+1.75-1.75 W m-1 K-1 respectively. The strong anisotropic thermal transport is attributed to the distinct atomic structures at altered chiral directions and direction-dependent group velocities. Thermal conductivities of 2D graphene sheets with the same dimensions are also computed for comparison. The extrapolated [small kappa] of the 2D graphene sheet are 1008.5+37.6-37.6 and 1086.9+59.1-59.1 W m-1 K-1 in the armchair and zigzag directions, respectively, which are an order of magnitude higher than those of phosphorene. The overall and decomposed phonon density of states (PDOS) are calculated in both structures to elucidate their thermal conductivity differences. In comparison with graphene, the vibrational frequencies that can be excited in phosphorene are severely limited. The temperature effect on the thermal conductivity of phosphorene and graphene sheets is investigated, which reveals a monotonic decreasing trend for both structures.