This paper presents the dynamic modeling and control of an over-actuated hexarotor with bounded rotor speeds. With actively tiltable propellers, the hexarotor can track six degrees of freedom (DOF) trajectories independently. Based on the state space model, a fast nonlinear model predictive controller (NMPC) using direct multiple shooting is proposed using two different non-linear programming solvers. The performance of the NMPC is analyzed using numerical simulations for step response and trajectory tracking under realistic operational conditions with noisy state estimation, parameter uncertainties, and disturbances. The controller is verified in the Gazebo simulator in a more realistic environment.