This paper presents a practical approach for a nonlinear model predictive control scheme with collision avoidance which is implemented on a mobile robot with two differential wheels. In model predictive control, also called receding horizon control, cost function is formulated to minimize tracking error. The optimal control input is solving a discrete nonlinear optimization problem over a pre-described prediction horizon based on a gradient descent method. Input and state constraints are implemented using a penalty function. The implemented controller minimizes the cost function through on-line optimization, making it possible to avoid obstacles with a natural and flexible trajectory. The tracking performance and the obstacle avoidance ability are verified through the realistic simulation.