An object of the invention is to provide a remote control system for robot in which a remotely controlled robot apparatus is capable of carrying out skillful movement and movement for removing a heavy load. A robot remote control apparatus 1 includes a remote instruction unit 4 for generating control data for the robot apparatus 2, a first computer unit for inputting and processing the control data, and a first mobile transmission unit for transmitting the control data to a base station 19 connected to a public transmission network 20; the robot apparatus 2 includes a second mobile transmission unit for receiving the control data transmitted from the base station 21 connected to the public transmission network 20 and a second computer unit for processing the control data and controlling a mechanism portion 10; the mechanism portion includes one or two heavy-load working arms, one or two light-load working arms, and a traveling system, all of which are controlled by the second computer unit; and the second computer unit controls the one or two heavy-load working arms, the one or two light-load working arms and the traveling system on the basis of the control data for the robot apparatus 2.