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In this paper, an optimal nonlinear feedback guidance algorithm with complex state and control constraints is developed for Mars powered decent. The analysis of the optimal control problem for Mars powered descent is undertaken firstly. Then based on the real-time sampling optimal feedback control theory, the Mars powered descent guidance (PDG) algorithm is designed and analysed. A practical method is also proposed to solve the problem of the initialization of the PDG algorithm. Numerical simulations are performed to evaluate the effectiveness of the proposed PDG algorithm. The effects of the sampling period and the prediction errors on landing errors are studied in the numerical simulations. The fuel consumption performances of the proposed PDG algorithm and the Apollo guidance algorithm are also studied and compared. The simulation results show that the less fuel consumption is obtained with the proposed PDG algorithm. Monte Carlo simulation verifies the high landing precision of the proposed PDG algorithm. [ABSTRACT FROM AUTHOR]