This paper presents the concept of a lifting-wing quadcopter unmanned aerial vehicle (UAV), a vertical take-off and landing vehicle (VTOL) with a rear wing, a canard at its front and four propellers. The aerodynamic surfaces are designed so that their mounting angle can be adjusted and fixed before flight, so its performance in transition flight can be studied for a combination of wing and canard mounting angles. A dynamic model using rigid-body equations of motion is presented, which is used to compute the transition flight trajectory from hover to cruise in horizontal flight. The trim conditions were computed for a range of fixed wing and canard mounting angles to study the effects of these variables on transition trajectory parameters such as required power, body pitch angle and propeller rotation speeds as a function of flight speed. Furthermore, a transition flight control algorithm is presented, which has a cascaded PID controller and a reference scheduler to switch between the proper reference states, controls and control allocation matrix. Finally, the transition control algorithm of the conceptual UAV is numerically simulated. Results show that this configuration can perform a fast and smooth transition from hover to cruise flight using the proposed flight control algorithm, substantially reducing required propulsive power in cruise of up to 64%. The application of the control algorithm made notable a transition manoeuver that consists of negatively inclining the aircraft at a negative pitch angle, initially at high intensity, and as the final cruising speed approaches, the inclination is attenuated until the equilibrium pitch angle is reached. Simultaneously with the negative inclination of the pitch angle, there is a slight drop in altitude, which is quickly resumed as the trajectory develops until the final cruising speed. Lastly, this aircraft configuration can be widely used in applications where performance gains in operations currently carried out by multicopters, which cover large distances and need long flight time, would bring great operational advantages.