In this paper, we consider the application of partial buffer sharing to an M/G/1/K queueing system for cognitive radio networks (CRNs). It is assumed that the CRN is subject to Nakagami-m. fading. Secondary users are allowed to utilize the licensed radio spectrum of the primary users through underlay spectrum access. A finite buffer at the secondary transmitter is partitioned into two regions, the first region serves both classes of packets while the second region serves only packets of the highest priority class. Therefore, the examined CRN can be modeled as an M/G/1/K queueing system using partial buffer sharing. An embedded Markov chain is applied to analyze the queueing behavior of the system. Utilizing the balance equations and the normalized equation, the equilibrium state distribution of the system at an arbitrary time instant can be found. This outcome is utilized to investigate the impact of queue length, arrival rates, and fading parameters on queueing performance measures such as blocking probability, throughput, mean packet transmission time, channel utilization, mean number of packets in the system, and mean packet waiting time for each class of packets.