Model Predictive Control (MPC) has gained widespread acceptance in industry due to its capability of coping with constraints, handling multiple-input-multiple-output systems and evolving control policy. One significant barrier to the development of MPC is its complexity in computation when encountering nonlinear systems, the resulting feedback delays, and the consequent loss of controller performance as well as stability issues. In this manuscript, we propose a new formulation of MPC for nonlinear systems based on Carleman linearization. The nonlinear dynamic constraints are modeled with bilinear representations. This formulation enables analytical computation of NMPC. Optimization is accelerated by providing sensitivity of the cost function to the control signals. A case study example using a nonlinear isothermal CSTR is presented, demonstrating that the proposed formulation reduces computational efforts.