As the robot based on a directly serial leg mechanism has great walking inertia and a larger weight/load ratio, a novel series-parallel hybrid quadruped walking robot is presented. The robot consists of a load platform and four serial-parallel legs. The kinematics characters of serial-parallel legs for the robot are analyzed. Each leg is connected by a hip, a thigh, a calf sequentially and the hip joint is a 3-RRR parallel mechanism. By considering the least energy-consuming posture as the optimal posture, the forward kinematics and inverse kinematics are derived based on vector method and they are verified by ADAMS and MATLAB softwares. The velocity Jacobian matrix and acceleration matrix of the serial-parallel hybrid leg are obtained based on vector method and differential transform method and their singularity is analyzed, then the workspace of the hybrid leg is figured out by MATLAB software. Calculations show that when the linkage diameters of the hip and thigh are 22 mm and 50 mm and the angle of knee θ4 is within ［105°, 155°］, the workspace of the hybrid leg is part of a sphere, whose radius of the inscribed circle R is 400 mm and altitude H is within［500 mm, 900 mm］. This research has great significance to a series of further studies on stiffness analysis, dynamic properties, mechanism optimal design and system control of the novel series-parallel quadruped walking robots.