Collaborative robots boast high flexibility, reliable safety, and strong human-machine collaboration capabilities. However, in practical operations, axis tilt errors can lead to decreased end-effector positioning accuracy, thereby affecting work performance and quality. To address this issue, this paper presents a kinematic model for collaborative robots that integrates Denavit-Hartenberg (DH) parameter errors with axis tilt errors. Initially referencing the DH method, the model establishes both the robot’s kinematic model and a parameter error model. It addresses issues unresolved by traditional non-geometric error compensation methods, namely the inability to establish a mapping relationship between the axis tilt joint positions in the calibration coordinate system and the end-effector positional errors. By utilizing the DH method and incorporating a generalized error matrix model, an improved kinematic model that includes tilt errors is proposed. This paper conducts forward kinematic analysis and employs the Newton-Raphson iteration method for inverse kinematics solutions. Simulation and experimental results demonstrate that, regardless of the influence of the tilt error matrix, the model accurately and effectively determines the end-effector pose and joint angles of the collaborative robot.