Achieving galloping gait in quadruped robots is challenging, because the galloping gait exhibits complex dynamical behaviors of a hybrid nonlinear under-actuated dynamic system. This paper presents a learning approach to quadruped robot galloping control. The control function is obtained through directly approximating real gait data by learning algorithm, without consideration of robot's model and environment where the robot is located. Three motion control parameters are chosen to determine the galloping process, and the deduced control function is learned iteratively with modified Locally Weighted Projection Regression (LWPR) algorithm. Experiments conducted upon the bioinspired quadruped robot, AgiDog, indicate that the robot can improve running performance continuously along the learning process, and adapt itself to model and environment uncertainties.