Step-climbing performance is an important index when evaluating the comprehensive performance of a planetary rover. Based on a comprehensive analysis of the existing planetary rover, the step-climbing performance was determined with regard to the suspension configuration of the rover. On the basis of the configuration of the parallel frame spring fork suspension, a multi-constraint quadrilateral suspension (MCQS) that is based on the λ (lambda) chain mechanism was proposed. The trajectory model of the end point of the λ linear mechanism was established, along with a mathematical model of the interaction between each wheel and step in the step-climbing process. A simulation model of the MCQS rover was constructed, and the step-climbing performance of the MCQS rover on a vertical obstacle was analyzed. The simulation results showed that the MCQS rover can climb over a step obstacle with a height larger than twice the wheel radius, and that it had superior integrated mobility. A prototype was developed based on the design and simulation, and some step-climbing experiments were performed to verify the performance of the MCQS rover.