In this work, we propose a mixed radio frequency (RF) and multiple-input-multiple-output (MIMO) free-space optical (FSO) system based on a variable-gain dual-hop relay transmission scheme. The RF channel is modeled by Rayleigh distribution and Gamma-Gamma turbulence distribution is adopted for the MIMO FSO link, which accounts for the equal gain combining diversity technique. Moreover, new closed-form mathematical formulas are obtained including the cumulative distribution function, probability density function, moment generating function, and moments of equivalent signal-to-noise ratio of the dual-hop relay system based on Meijer's G function. As such, we derive the novel analytical expressions of the outage probability, the higher-order fading, and the average bit error rate for a range of modulations in terms of Meijer's G function. Furthermore, the exact closed-form formula of the ergodic capacity is derived based on the bivariate Meijer's G function. The evaluation and simulation are provided for system performance, and the effect of spatial diversity technique is discussed as well.