An overwhelming majority of the existing work on spectrum sensing assumes that secondary users (SUs) are stationary. However, mobility is an essential property of wireless networks. In this paper, we analyze the performance of spectrum sensing by mobile SUs. Four performance metrics, i.e. detection, miss detection, false alarm and error probabilities, are thoroughly investigated. A critical variable for spectrum sensing in mobile cognitive radio networks (CRNs) is the received primary user signal power (RPUP) by a mobile SU. We model this power mathematically, and then derive its probability distribution and mathematical expectation. At last, the expressions are derived for those four performance metrics. We perform extensive numerical simulations, finding out that the results are consistent with our theoretical analysis. It is concluded that the SU mobility has significant effects on the detection, miss detection and error probabilities, but dose not affect the false alarm probability.