The objective of this paper is to present an online trajectory tracking based on model predictive control for service robot. The key point of model predictive control (MPC) algorithm is to consider an on-line optimization problem so as to obtain the optimal control input sequence in a specific time period. The main characteristics of MPC are only the first element of the control sequence is implemented as the current control input in the repeated calculations. Hence, it is more suitable for time-varying systems than conventional infinite horizon control. In this paper, explicit model predictive controller is applied to a Dual-arm Service Robot (Panda Robot) developed in our NTU-iCeiRA Lab. There are six Degrees-of-freedom for each arm, which is capable of achieving desired tasks. The proposed method is able to control the movement of each axes based on the information itself to minimize the performance index that we choose. Moreover, in order to decrease the effect of jerky motion, we apply an on-line trajectory generator to obtain a smooth trajectory by the constraints of velocity and acceleration. Experimental results demonstrate that the proposed control scheme is able to increase the positioning accuracy.