Geometric errors such as inaccurate link length and assembly alignment are the primary sources of positioning errors for industrial robots. Besides, complex joint-dependent kinematic errors in the bearing system and harmonic drives are also non-negligible. The robot is regarded as an ideal rigid body in typical kinematic models, which can only describe the influence of geometric errors. This paper proposes a generalized kinematic error model based on product of exponentials (POE) formula, which contains constant geometric errors and complex joint-dependent kinematic errors. The unknown model parameters are identified with the Levenberg-Marquardt method. Experiments are implemented on an Efort ECR5 robot to validate the effectiveness of the proposed model. In these experiments, we use 250 measurements as the identification data set for parameter identification, and other 100 measurements are utilized to validate the accuracy of the proposed model. These experiments display that the proposed model can reduce the mean position error of the Efort ECR5 robot from 2.014 mm to 0.115 mm on the validation data set. Experimental results prove that the proposed model can describe the kinematics of industrial robots with high accuracy.