We introduce a simple growth model which exhibits a first-order pinning-depinning (PD) transition in disordered media. In our model, a first-order PD transition is triggered by the local inertia force Fl=pLv̅ , where p denotes a constant between 0 and 1, L is the system size, and v̅ is the average velocity in a local region of the growing interface. If p<pc, our model shows a continuous PD transition. However, if p>pc, our model shows a first-order PD transition. We measure the critical exponents characterizing the dynamical behavior of our model and explain how a first-order PD transition can occur if p>pc. Besides the PD transitions, our model exhibits another phase transition from a fluctuating to a nonfluctuating interface with a constant velocity.