This paper presents the design method a proportional integral derivative (PID) controller with time-varying parameters for trajectory tracking of a mecanum-wheeled robot with a minor error. First, a nonlinear kinematic error model of the robot is established and linearized around the working point. Then a PID controller with time-varying parameters is designed based on this linear model. The coefficients of KP, KI, and KD control parameters are determined by trial and error technique to ensure that the robot moves along the desired trajectory with minimal error. A platform mecanum-wheeled mobile robot has been designed and manufactured to demonstrate the proposed controller. Simulation and experimental results are presented to verify the effective and accuracy of the proposed controller. It shows that can apply this research to control of a four mecanum-wheeled mobile robot in logistics services in practice.