We propose a p-persistent protocol for slow-frequency-hopped slotted random access networks, assuming that all the users know the number of backlog users in a slot. The proposed protocol delays new packet transmission until the number of users with a packet to be retransmitted decreases to the threshold or less. Performance of the proposed protocol is evaluated with a two-dimensional Markov chain for systems with finite population in terms of throughput efficiency and the average transmission delay. Numerical results show that the proposed protocol can achieve better performance by suppressing new packet transmission, compared to the conventional frequency-hopped slotted ALOHA. The optimum value of the threshold is also numerically derived.