The inspiration for the footed robot was originally derived from biology, and it was an imitation of biological form and movement. In this paper, a bionic-robot dog is designed to reveal the motion characteristics of a quadruped robot mechanism through modeling, model kinematic analysis, and other methods. First, the structural characteristics and movement characteristics of the developed bionic-dog model are studied. The first step is to study the physiological structure of the dog, analyze the function of the dog’s limbs, and then use a high-speed camera to capture the motion of the marked bionic-robot dog and shoot motion video of the bionic-robot dog in different motion states. The effective data of the marked points in the video are extracted using PHOTRON 1.0 software, and the extracted data are analyzed and processed in the software MATLAB R2020a, and finally the structural characteristics and motion laws of the bionic-robot dog are obtained. Then, a bionic-robot-dog experimental platform is built to conduct experiments with three planned gaits (dynamic gait, static gait, and gait transition). The experiments showed that the three gaits were consistent with the planned movements and the bionic-robot dog could perform stable fast-gait walking, slow-gait walking, and quickly complete gait transitions. All three gaits were simulated in ADAMS 2019 software, and the simulation results showed that all three gaits caused the bionic dog robot to move smoothly.