In this paper we designed a high speed wireless multiple access protocol, which is suitable for future multimedia wireless LAN systems which support high quality video teleconferencing, telephony and graphic databases. In the proposed protocol, Slotted-ALOHA protocol is used for transmitting random data packets and the packet reservation multiple access(PRMA) protocol for transmitting periodic data packets. The use of minislot is introduced for the reservation scheme. In order to measure the performance characteristic of the proposed protocol, a simulator is designed using an object oriented programming language, C++, and an exhaustive simulation study is carried out. From the simulation results, it is observed that the proposed protocol and the existing PRMA protocol have almost the same delay characteristic when network traffic is low. However, the proposed protocol is superior to the PRMA protocol when traffic becomes higher. The proposed protocol and the results can be utilized for the design of the wireless access systems and future broadband wireless LANs.