Majority of today's fixed-pitch, electric-power quadrotors have short flight endurance ($<$ 1 hour) which greatly limits their applications. This paper presents a design methodology for the construction of a long-endurance quadrotor using variable-pitch rotors and a gasoline-engine. The methodology consists of three aspects. Firstly, the rotor blades and gasoline engine are selected as a pair, so that sufficient lift can be comfortably provided by the engine. Secondly, drivetrain and airframe are designed. Major challenges include airframe vibration minimization and power transmission from one engine to four rotors while keeping alternate rotors contra-rotating. Lastly, a PD controller is tuned to facilitate preliminary flight tests. The methodology has been verified by the construction and successful flight of our gasoline quadrotor prototype, which is designed to have a flight time of 2 to 3 hours and a maximum take-off weight of 10 kg.