This paper proposes a method to surpass the computational hurdles associated with nonlinear model predictive control (NMPC) via a formulation of advanced-step bilinear Carleman approximation-based MPC (ACMPC). This formulation is a combination of bilinear Carleman approximation (also known as Carleman linearization) based MPC (BCMPC) and advanced-step nonlinear MPC (asNMPC). It takes action based on a prediction of the future initial state, reduces the amount of computation by analytically predicting future system behavior and providing the sensitivity of the cost function to the manipulated variables as the search gradient. Through a linear approximation, it updates the pre-calculated optimal control signals as soon as the real system states are obtained on-line. Thus, it significantly reduces the required time of computing the optimal control signals on-line before they are injected into the system. Regulating an open loop unstable CSTR under disturbance is illustrated as a case-study example.