The venous blood test is a prevalent auxiliary medical diagnostic method. Venous blood collection equipment can improve blood collection’s success rate and stability, reduce the workload of medical staff, and improve the efficiency of diagnosis and treatment. This study proposed a rigid-flexible composite puncture (RFCP) strategy, based on which a small 7-degree-of-freedom (DOF) auxiliary venipuncture blood collection (VPBC) robot using a trocar needle was designed. The robot consists of a position and orientation adjustment mechanism and a RFCP end-effector, which can perform RFCP to avoid piercing the blood vessel’s lower wall during puncture. The inverse kinematics solution and validation of the robot were analyzed based on the differential evolution algorithm, after which the quintic polynomial interpolation algorithm was applied to achieve the robot trajectory planning control. Finally, the VPBC robot prototype was developed for experiments. The trajectory planning experiment verified the correctness of the inverse kinematics solution and trajectory planning, and the composite puncture blood collection experiment verified the feasibility of the RFCP strategy.