An address competition method of a multi-connection type control system, intended to solve the problem of how to increase the efficiency of indoor air-conditioner unit address configuration where, according to the order in which a first slave control device initiates an address request, a relay device allocates, in sequence, temporary addresses to all first slave control devices, and according to the temporary addresses, initiates address requests in sequence to a master control device; according to the order in which a second slave control device initiates an address request, the master control device allocates, in sequence, official addresses to all second slave control devices; according to the temporary addresses, the relay device allocates the official addresses to the corresponding first slave control devices. The method can efficiently allocate an address to an indoor air-conditioner unit, and ensures that the address of each indoor air-conditioner unit is unique.