Fog radio access networks (F-RAN) is used to meet high requirements of the fifth-generation (5G) mobile communication. With scale of terminals expanded, frequency spectrum becomes a bottleneck of developing F-RANs, and traditional orthogonal multiple access (OMA) is not highly effective on resource utilization. To improve spectrum efficiency, sparse code division multiple access (SCMA) is presented as a promising technique. In this paper, the performance of a SCMA-based scheme in F-RANs is evaluated. In particular, a lower bound of the average outage probability of a typical user is provided based on stochastic geometry, which can give some insights on how to improve the transmission reliability of SCMA. Meanwhile, a lower bound of capacity on a subcarrier is derived. Simulation results are provided to validate the accuracy of analysis and show the performance gain of SCMA compared with OMA.