In scenarios of manufacturing and high-precision operations, achieving high positioning accuracy of industrial robots is crucial. Kinematic calibration plays a vital role in reducing positioning errors. Considering both the geometric errors introduced by the machining and assembly processes and the joint compliance errors stemming from gearboxes, this paper establishes an elasto-geometrical error model based on the robot MDH model and the joint compliance model, and only position errors are required for calibration. The established model enables the identification of kinematic parameters, transformation frame parameters, and all joint stiffness under external loads. Furthermore, a hybrid calibration algorithm is proposed by combining least squares and heuristic algorithms, and redundancy is then analyzed and eliminated to further improve accuracy. By designing the hybrid algorithm, the proposed method can converge to the optimal solution quickly while maintaining sufficient global search capabilities. Finally, a simulation is conducted and the absolute positioning error decreases from 2.8658 mm to 0.1682 mm, validating the effectiveness of the proposed model and algorithm.