Within the scope of LRS Bianchi type-I cosmological model the role of spinor field on the evolution of the Universe is investigated. In doing so, we have considered a polynomial type of nonlinearity. It is found that depending on the sign of self-coupling constant the model allows either accelerated mode of expansion or oscillatory mode of evolution. While the non-diagonal components of the energy-momentum tensor of the spinor field in case of a full Bianchi type-I model leading to the vanishing mass and nonlinear term in the spinor field Lagrangian, in case of an LRS Bianchi type-I model neither mass term nor the nonlinear term of spinor field vanish.The accepted manuscript in pdf format is listed with the files at the bottom of this pag...