Spectrum sharing cognitive radio (CR) with maximal ratio combining (MRC) diversity under asymmetric fading is studied. Specifically, the channel on the secondary transmitter (STx) to the secondary receiver (SRx) link is Nakagami-m distributed while the channel on the STx to the primary receiver (PRx) link is Rayleigh distributed, and the channel state information (CSI) on the STx-PRx link is assumed to be outdated due to feedback delay. The outage capacity of the secondary user (SU) is derived under the average interference and peak transmit power constraints. The results supported by simulations are presented and show the effects of various system parameters on the outage capacity. Particularly, it is shown that the outdated CSI has no impact on the outage capacities in the cases of low peak transmit power constraint and zero-outage probability. It is also shown that MRC diversity can significantly improve the outage capacity especially for the zero-outage capacity and the outage capacity under low outage probability.