Deterministic Adaptive Priority Network Access Delay （DAP-NAD） provides prior access for network nodes by using token ring. The First Station Number （FSN） of this algorithm goes forward one by one with the step of 1， introducing many empty slots within each Network Access Period （NAP）， so that channel resources were wasted. DAP-NAD-R algorithm was proposed to solve the above problem. Firstly， FSN step was modified from 1 to R to jump over the nodes that had got prior network access in previous NAP. Secondly， B slot was introduced to meet the communication requirement of nodes being jumped over. In specific， those nodes were able to send an emergent short frame to stop the corresponding jump. Finally， the fact is that multicast communication is a typical application of combat network radio. To make prior access for multicast source node， DAP-NAD-R algorithm was further modified. In this way， the multicast source node was able to also send the emergent short frame in B slot， and after nodes of each station receiving the short frame， network access opportunity was transferred to the multicast source node at first. Simulation results show that compared with DAP-NAD-R algorithm， the modified algorithm for multicast decreases the End-To-End delay （ETE） and the lost rate of voice packet by 10% and 15%， respectively. DAP-NAD-R algorithm and its modified algorithm are suitable for combat network radio with simultaneous voice and data transmission， decreasing the delay for data packet with high priority and the lost rate of voice packet significantly， so as to increases the efficiency of multicast communications.