The non-collision packet reservation multiple access (NC-PRMA) protocol has been proposed for wireless voice communications. In that protocol, although it can avoid any collision by using control minislot, the terminal which generates its talkspurt in current frame has to wait till a next frame to transmit a request minipacket to obtain reservation. In this paper, we propose the NC-PRMA with random transmission to idle slot to reduce mean access delay. We evaluate the mean access delay and the voice packet dropping probability by the theoretical analysis. We also evaluate the total throughput by the computer simulation. It is shown that the proposed scheme attains lower mean access delay than conventional NC-PRMA.