The invention relates to the technical field of hoisting equipment, and discloses a constant-pressure friction driving trolley of hanging type hoisting equipment and a method. The constant-pressure friction driving trolley comprises a hanging type trolley bearing device and a hanging type trolley driving device, wherein the hanging type trolley bearing device hung on a running rail is fixedly connected with the hanging type trolley driving device and is formed by connecting end beams clamped on two sides of the running rail with guide wheel devices and bearing wheel devices which are arranged on the end beams. Friction of running wheels is not related to the hoisting weight, the gravity and the stress, and the friction driving force of the running wheels is only related to pressure of a spring instead of being related to stress of a girder; therefore, the wheels run synchronously, and a phenomenon of rail gnawing is avoided; the service life of a motor is well prolonged; the constant-pressure friction driving trolley is small in size, light in mass, high in bearing capacity and anti-abrasion; and the problem of large noise during running is completely solved; and constant driving force is guaranteed.