This research is concerned with an adaptive controller of a mobile manipulator for moving operation while traveling on an unknown irregular terrain. Considering a requirement of traveling operation that the end-effector of the mobile manipulator tracks a desired trajectory in the vehicle-fixed coordinates while the mobile manipulator is traveling on an unknown irregular terrain, the mobile manipulator is subjected to effects of disturbance torques derived from both static and dynamic influences depending on the irregularity and the motion through reaction force and torque from the terrain. We show experimentally that an adaptive controller with a neural network can compensate such kinds of unknown disturbances. The validity of the neuro-adaptive controller is clarified through real experiments, which compare the simple adaptive controller and neuro-adaptive controller in two different conditions, which are horizontal and irregular terrain. The results show that the trajectory-tracking accuracy while traveling on the unknown irregular terrain is possible to be maintained almost to the same accuracy as it is traveling on horizontal plane.