Recently, mobility support of connectionless mobile ATM data service has been mainly studied in wireless ATM communication network. this paper shows the network model for the mobility support of connectionless data service in ATM network, and proposes the methods to minimize COIP (care of IP address) acquisition processing time for MH(mobile host)migration. Th echaracteristics of proposed methods, COIP acquisition probability and IP data communication sequence of proposed model, are discussed in this paper.