In order to make the trajectory of the robot continuous and smooth during the operation, the kinematics analysis and trajectory planning of a 6 Degree of Freedom (DOF) robot are performed. Taking a 6-DOF UR10 robot as the research object, based on the homogenous transformation theory of rigid body motion, the UR10 robot was modeled by using the modified D-H method, the robots forward and inverse kinematics were analyzed based on geometric method with algebraic method. The mapping relationship between the pose of the end effector in Catesian space and robot joint angle in joint space was obtained, and the accuracy of formula derivation was verified by an example. Finally, based on the MATLAB robotics toolbox, the trajectory planning simulation experiment of the UR10 robot was performed by using the trapezoidal speed hybrid curve. The experimental results show that the trajectory planning based on the trapezoidal velocity hybrid curve achieves the continuous and smooth motion trajectory of the robot.