Considering the economically optimal control problem of constrained nonlinear systems, this paper proposes an economic model predictive control(EMPC) scheme with guaranteed input-to-state stability(ISS) on economic performance. An optimally economic steady-state point of the system is computed offline and then a stabilizing optimal control problem is formulated to track the steady-state point. Moreover, the optimal value function of the stabilizing optimal control problem and the relaxed index of the economic performance are used to design the contracive constraint of the EMPC optimization problem. Then the invariant-set principle and the ISS theorem are combined to establish recursive feasibility of the EMPC and ISS of the closed-loop system on economic performance. Finally, the simulation comparison results on the control of a nonlinear continuously stirred tank reactor are used to verify the effectiveness of the proposed scheme.