A composite valve has a communication path, a second valve port and a pilot passage. First and second valve bodies are arranged to be moved up and down in the same direction, and are away from each other only at a predetermined distance. In the case that a lift amount of the second valve body for a small flow rate control is equal to or less than a predetermined amount, said pilot passage and a first valve port are respectively closed by a pilot valve body and the first valve body, thereby taking a small flow rate control state. In the case that the lift amount of said second valve body goes beyond said predetermined amount, said pilot valve body is moved up by the upward movement of a valve shaft to open said pilot passage, thereby taking a large flow rate control state.