Exploring Mars is beneficial to increasing our knowledge, understanding the possibility of ancient microbial life there, and discovering new resources beyond the Earth to prepare for future human missions to Mars. To assist ambitious uncrewed missions to Mars, specific types of planetary rovers have been developed for performing tasks on Mars’ surface. Due to the fact that the surface is composed of granular soils and rocks of various sizes, contemporary rovers can have difficulties in moving on soft soils and climbing over rocks. To overcome such difficulties, this research develops a quadruped creeping robot inspired by the locomotion characteristics of the desert lizard. This biomimetic robot features a flexible spine, which allows swinging movements during locomotion. The leg structure utilizes a four-linkage mechanism, which ensures a steady lifting motion. The foot consists of an active ankle and a round pad with four flexible toes that are effective in grasping soils and rocks. To determine robot motions, kinematic models relating to foot, leg, and spine are established. Moreover, the coordinated motions between the trunk spine and leg are numerically verified. In addition, the mobility on granular soils and rocky surface are experimentally demonstrated, which can imply that this biomimetic robot is suitable for Mars surface terrains.