A method for robot demonstration learning based on forward hidden Markov models is proposed to address the problems of low parameter estimation efficiency and poor trajectory reconstruction accuracy in the process of robot demonstration trajectory encoding. The method identifies key points of multiple collected demonstration trajectories using the Linde-Buzo-Gray ( LBG) algorithm, selects appropriate trajectory calculation model initialization parameters using the minimum distortion criterion, and completes model parameter estimation by combining the Baum-Welch algorithm. On this basis, the Viterbi algorithm is used to calculate the most likely attribution state of each sample point, and the maximum likelihood estimation is utilized to recalculate the state parameters of each sample point attributed to each state. Finally, the reconstructed trajectory is obtained through Gaussian mixture regression. To evaluate the effectiveness of the algorithm, a handwritten letter trajectory dataset and a demonstration learning experiment of wafer mechanical arm automatic feeding trajectory are designed. The average Fr􀆧chet distance is introduced to quantitatively evaluate the trajectory reconstruction accuracy. The experimental results show that the proposed method improves the trajectory reconstruction accuracy by 15. 15% compared to traditional methods, with an average Fr􀆧chet distance of 5. 49 in the automatic wafer loading trajectory of the robotic arm,which indicates promising application prospects.