This paper presents a performance analysis for the average channel capacity of an asymmetric two-hop cooperative relaying in cognitive-radio system, in which the first hop is a radio-frequency (RF) link and the second hop is a free-space-optical (FSO) communication link. In the considered cognitive radio, the licence spectrum of a primary user (PU)is shared with an unlicensed user, denoted as secondary user (SU), using underlay spectrum-sharing and power control mechanism to keep the interference at the PU receiver side, always below a given threshold. For the FSO link, some practical issues such as pointing errors, and atmospheric turbulence are taken into considerations, where the IM/DD scheme is used for signal detection. It is also assumed that RF and FSO links follow the Rayleigh and the Gamma-Gamma distributions, respectively. To perform a performance analysis, the cumulative distribution function (CDF) of the received signal-to-noise-ratio (SNR) at the SU receiver is presented. Using the CDF expression, a closed-form expression is derived for the average channel capacity of the considered hybrid RF-FSO system. Finally, the numerical results as well as Monte-Carlo simulation results, and discussions are presented.