In this paper, a contention-based reservation access control algorithm and a slot allocation algorithm are proposed for non-real-time bursty traffic services in the wireless ATM networks. In order to reduce the collisions of the reservation request packets, the base station scheduler calculates the transmission probability using the number of RAS minislots and the estimated load of the reservation request packets. And it broadcasts the calculated transmission probability over the downlink control channel. Mobile terminals, which have traffic burst, select randomly a RAS minislot and transmit the reservation request packet by the received transmission probability. The reservation request packet contains the number of packets in the buffer. The slot allocation is based on the buffer status of the received reservation request packets. The base station scheduler allocates slots in proportion to the total number of slots that are requested by each terminal.