In this paper, a space reactor core dynamics is identified online by a recursive least-squares method. Based on this identified reactor model consisting of the control reactivity and the thermal electric generator power, the future thermoelectric (TE) generator power is predicted. A model predictive control method is applied to design an automatic controller for TE generator power control for a space reactor of the SP-100 system. The basic concept of the model predictive control is to solve an optimization problem for a finite future at current time and to implement as the current control input only the first optimal control input among the solutions of the finite time steps. At the next time step, the procedure to solve the optimization problem is then repeated. The objectives of the proposed model predictive controller are to minimize both the difference between the predicted TE generator power and the desired power and the variation of the control reactivity. Also, the control constraints are subjected to maximum and minimum reactivity and to maximum reactivity change. Therefore, the genetic algorithm that is appropriate to accomplish multiple objectives is used to optimize the model predictive controller. A lumped parameter simulation model of the SP-100 nuclear space reactor is used to verify the proposed controller. The results of numerical simulation to check the performance of the proposed controller show that the TE generator power level controlled by the proposed controller could track the target power level effectively, satisfying all control constraints.