A longitudinal altitude and attitude controller is designed for an unmanned aerial vehicle to detect landmines. The UAV considered in this study has two front rotors, two rear rotors, and elevons. Due to the characteristics of the mine detection sensor, the allowable pitch change of the UAV is strictly limited. Therefore, the attitude controller considering the pitch-hold constraint should be designed. To deal with a flight path angle change limit due to the pitch-hold constraint and accurate altitude tracking, a linear model predictive control method is used for altitude control design. Numerical simulation is carried out to demonstrate the performance of the proposed controller.