The accuracy of industrial robots is critical in many manufacturing applications. In this case, a self-developed automated fiber placement heavy-duty robot is used for the lay-up of carbon fiber composite prepregs, which requires high positioning accuracy. The mass of the robot body and end-effector exceeds 3 tons and 1 ton, respectively, resulting in considerable deformation and other errors due to the huge size and mass. Paradoxically, the work that our robot engaged in requires high precision, and the positioning accuracy needs to be less than 0.5 mm. This paper conducts a comprehensive analysis of the robot joint error, so as to improve the accuracy of the robot. A torsional and capsize deformation model for joints is established. In addition, the capsize torque and capsize axis of joint deformation are derived to determine the transformation relationship between joint frames. Chebyshev polynomials are used to describe joint-dependent errors. The Levenberg–Marquarelt (L–M) algorithm was used to identify the error model parameters. The effects of different error factors on the positioning accuracy were compared and analyzed. The validation result shows that the proposed model describes 88.11% of the positioning error, and the average residual error of the calibration can reach 0.132 mm. The identified joint-dependent error and the compliance error are 0.296 mm and 0.240 mm, accounting for 26.67% and 21.62% of the positioning error, respectively.