In this paper, a novel 3D (three-dimensional) soft-landing dynamic theoretical model of a legged lander is developed in detail as well as its numerical solution process. The six degrees of freedom motion (6-DOF) of the base model of the lander with mass center offset setting is considered in the model as well as the spatial motion (3-DOF) of each landing gear. The characteristics of the buffering force, the footpad–ground contact, and the inter-structure friction are also taken into account during the motion of each landing gear. The direct constraint violation correction is used to control the constraint stabilization of the nonlinear dynamic equation. Comparative studies between the results from the proposed model and the simulated model (built in MSC Adams) under four classical load cases show the validity of the model. Additionally, the influences of different types of contact force models, friction force models, and a friction correction model used in the soft-landing dynamic model are further investigated as a step toward understanding the soft-landing dynamic performance and the feasibility of the dynamic model method of a legged lander. The results indicate that a precise lateral force model of the footpad–ground contact is necessary to obtain the soft-landing performance of one lander during soft landing.