The supercritical water reactor is one of the six reactors recommended by the Generation IV International Forum. Compared with existing light water reactors,it enjoys advantages of high thermal efficiency, simplified system structure and low cost. The physical model of the supercritical water reactor is established with the MCNP program in this paper, with consideration of the variations of the coolant density along the axial and the intricate geometry of the fuel assembly. Based on the core model of the supercritical water reactor, the radial neutron flux density distribution of the core is calculated and a design scheme of the flattening power distribution is proposed. The axial neutron flux density distribution of the core is calculated, and the effect of the control rod on the peak shift of the axial neutron flux density is discussed. It is suggested that the control rod of the supercritical water reactor should be inserted up from the bottom. This paper provides some food of thought for the construction and the security analysis of the supercritical water reactor, as well as for the application and the development of the supercritical water reactor.