The performance of dual-hop mixed radio frequency (RF)/free space optical (FSO) communication system with partially coherent beams (PCBs) is investigated on the basis of decode-and-forward (DF) protocol. Specifically, both the RF and FSO channels are assumed to follow F-distribution with proper selection of parameters. Taking the path loss, atmospheric turbulence, and pointing errors into consideration, the closed-form expressions for the probability density function (PDF) and cumulative distribution function of the received signal-to-noise ratio are derived in terms of hypergeometric function in RF and FSO links, respectively. Subsequently, the closed-form expressions for outage probability, average bit error rate, and ergodic channel capacity of this system with M-ary phase-shift keying and M-ary quadrature amplitude modulation schemes are obtained on the basis of DF protocol. The results show that shadowing in RF link as well as the pointing error and atmospheric turbulence in FSO link would result in significant performance deterioration in dual-hop mixed RF/FSO system, while PCB can bring significant performance improvement of mixed RF/FSO systems with pointing errors over weak to moderate turbulence. Furthermore, the correctness of the analytical expressions is verified by Monte Carlo simulations. This work would benefit the design and development of the mixed RF/FSO systems.