In this paper, a Nonlinear Model Predictive Control (NMPC) has been employed to solve point-stabilization problems with static and dynamic obstacles avoidance. The algorithm was implemented on a mobile robot with two differential drive wheels. In NMPC, a cost function is formulated to minimize an error between the reference and the current state of the system subject to constraints. The major drawback of NMPC is the computation time, which results from predicting the system's state over a horizon. However, in this work, the resulting optimal control problem is converted to a discrete nonlinear programming problem using a recently developed toolkit. Dynamic obstacles avoidance is incorporated as a time-varying constraint and can be affected by a short prediction horizon. On the other hand, a long prediction horizon affects the computation time. For this, a terminal state penalty is added to the cost function to guarantee the stability of the control using a relatively shorter prediction horizon. The performance of the proposed controller achieving both static and dynamic obstacles avoidance is verified using several simulation scenarios.