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The performance of carrier sense multiple access (CSMA) in an unslotted multi-channel cognitive radio network under non-saturation condition is studied. In this system, every secondary user in idle state generates a new file after exponential distributed time and randomly generates a file which consists of geometrically distributed number of packets. We model the above described unslotted cognitive radio network by retrial queueing system with 3-dimensional continuous time markov chain(CTMC) and obtain the steady state probability of the CTMC using matrix analytic method. We obtain performance measures such as the throughput of SUs and the loss probability of SUs. Numerical results show that the file size and the file generation rate of SUs impact on the performance of CSMA under non-saturation condition significantly. [ABSTRACT FROM PUBLISHER]