The tilt-rotor quadcopter is an optimized structure of the standard quadcopter, which has actuating motors that can tilt about the quadcopter arm. A tilt-rotor quadcopter with more control inputs could theoretically bring stronger anti-disturbance and fault tolerance capabilities and track along a given path while maintaining a desired attitude. In this paper, a tilt-rotor quadcopter prototype is presented, whose actuator groups are independently tilted by motor servo systems. A non-linear model predictive control is further designed to allocate the inputs for actuating motors and tilting motors while solving the pathfollowing problem of a drone. Numerical simulations were run with different disturbances on the tilt-rotor quadcopter model, whose dynamics are presented according to the real quadcopter prototype. The simulation studies show the redundant control volume of the tilt-rotor quadcopter can bring stronger antidisturbance capabilities and more flexible path-tracking ability to the quadcopter, as well as demonstrate the effectiveness of the control allocation by non-linear model predictive control.