Robot dynamics and its parameter identification are of great significance to the realization of optimal control and human–machine interaction. The objective of this research is to address the shortcomings of establishing and identifying the self-developed six-degree-of-freedom (6-DoF) collaborative robot dynamics, which leads to a large error in the predicted torque of the proposed robot. A long short-term memory (LSTM) in an optimized recurrent neural network (RNN) is proposed to compensate the dynamic model of the proposed 6-DoF collaborative robot based on the consideration of gravity, Coriolis force, inertial force, and friction force. The analysis and experimental findings provide promising results. The compensated collaborative robot dynamic model based on LSTM in an optimized RNN displays a good prediction on the actual torque, and the root-mean-square (RMS) error between predicted and actual torques are reduced by 61.8% to 78.9% compared to the traditional dynamic model. Results of the experimental applications demonstrate the validity of the proposed systematic error compensation strategy.