In this work, we present the non-linear elasto-plastic phase-field model and simulation of the martensitic transformation in a polycrystalline material including the effects of grain and twin boundaries. The phase-field microelasticity theory proposed by Khachaturyan is used to perform 2D and 3D simulations of fcc -> bct martensitic transformation in a Fe-0.3%C polycrystalline alloy, incorporating the effect of both coherent and incoherent boundaries. The effect of plastic accommodation is also introduced into the model, by solving a time-dependent equation, during the solid-to-solid phase transformation. It is found that the given phase-field model, with the effect of grain boundaries, not only respects the morphological features of martensite but also conforms well with the physics of the problem. Different sets of simulations are performed to validate the model and it is concluded that the given model can correctly predict the evolution of the martensitic microstructure in a polycrystal, as opposed to previous models where the effects of grain and twin boundaries are neglected.