Large scale graphene sheets and other two-dimensional (2D) materials are commonly fabricated via chemical vapor deposition (CVD) technique which produces polycrystalline samples wherein Kapitza conductance along grain boundaries may substantially affect thermal transport. In this work, thermal conductivity of polycrystalline graphene (PG) was explored with grain sizes ranging from 2 nm to 10 nm employing non-equilibrium molecular dynamics (NEMD) simulations. Kapitza conductance at grain boundaries was estimated by fitting continuum models to the NEMD results. By calculating 2D temperature profile, both NEMD and continuum models show that Kapitza resistance is the dominant factor in thermal transport within PG with small grain sizes. Effects of nitrogen and boron doping and compressive and tensile strain on effective thermal conductivity of PG nanomembranes were further investigated. The results showed that, doping affects neither the Kapitza conductance nor the thermal conductivity of PG with nano-sized grains. Moreover, applying strain to PG in two directions, namely parallel and normal to the heat flow direction, suppress the thermal conductivity by increasing the grain size. The obtained results can provide useful understanding about heat transport not only in the polycrystalline graphene, but also in other CVD-grown 2D materials. (C) 2018 Elsevier Ltd. All rights reserved.