The purpose of cognitive radio (CR) technology is to improve spectrum utilization. In recent years, dynamic spectrum access (DSA) has become one of critical researches for achieving improved transmission performance in CR. A rendezvous algorithm facilitates a connection between a pair of secondary users (SUs) to achieve peer to peer transmission in CR environment. Most researchers have adopted the rendezvous degree and the time to rendezvous (TTR) as key factors to design rendezvous algorithms. However, the occurrence of a primary user (PU) can shield off the rendezvous even when both SUs occupy the same channel. A complete peer to peer transmission process in cognitive radio network (CRN) provides not only rendezvous for SUs but also channel access for data transmission under priority usage of PU. This paper proposes an algorithm to achieve shift-based channel hopping for continuous rendezvous (SCHCR) to guarantee that each SU can rendezvous continuously with its receiver within the upper bound of the expected TTR without a centralized control mechanism. This continuity property facilitates rendezvous, particularly when PUs exist. Based on the rendezvous algorithm, this paper further proposes a threshold controlled skip (TCS) scheme and two policies for the occurrence of PU to resolve channel contention and data transmission problems. Simulation results indicated that the proposed schemes achieve shorter rendezvous time, particularly when the load of PU is high, and facilitate superior transmission performance.