Purpose The paper aims to reduce the low-frequency resonance and residual vibration of the robot during the operation, improve the working accuracy and efficiency. A reduced weight and large load-to-weight ratio can improve the practical application of a collaborative robot. However, flexibility caused by the reduced weight and large load-to-weight ratio leads to low-frequency resonance and residual vibration during the operation of the robot, which reduces the working accuracy and efficiency. The vibrations of the collaborative robot are suppressed using a modified trajectory-planning method. Design/methodology/approach A rigid-flexible coupling dynamics model of the collaborative robot is established using the finite element and Lagrange methods, and the vibration equation of the robot is derived. Trajectory planning is performed with the excitation force as the optimization objective, and the trajectory planning method is modified to reduce the vibration of the collaborative robot and ensure the precision of the robot terminal. Findings The vibration amplitude is reduced by 80%. The maximum torque amplitude of the joint before the vibration suppression reaches 50 N center dot m. After vibration suppression, the maximum torque amplitude of the joint is 10 N center dot m, and the resonance phenomenon is eliminated during the operation process. Consequently, the effectiveness of the modified trajectory planning method is verified, where the vibration and residual vibration in the movement of the collaborative robot are significantly reduced, and the positioning accuracy and working efficiency of the robot are improved. Originality/value This method can greatly reduce the vibration and residual vibration of the collaborative robot, improve the positioning accuracy and work efficiency and promote the rapid application and development of collaborative robots in the industrial and service fields.