Stationary source inverse-geometry CT (SS-IGCT) has been proposed as a new system architecture that has several key advantages over traditional cone beam CT (CBCT). One advantage is the potential for acquiring a large volume of interest with minimal cone-beam artifacts and with very high temporal resolution. We anticipate that SS-IGCT will use large, stationary source arrays, with gaps in between separate source array modules. These gaps make reconstruction challenging because most analytic reconstruction algorithms assume a continuous source trajectory. SS-IGCT is capable of producing the same dataset as a traditional scanner taking multiple overlapping axial scans, but with segments of the views missing from each axial scan because of gaps. We propose the following, two-stage volumetric reconstruction algorithm. In the first stage, the missing rays are estimated in a spatially varying fashion using available data and geometric considerations, and reconstruction proceeds with standard algorithms. The missing data are then re-estimated by a forward projection step. These new estimates are quite good and the reconstruction can be performed again using any algorithm that supports multiple parallel axial scans. Although inspired by iterative reconstruction, our algorithm only needs one "iteration" of forward- and back-projection in practice and is efficient. Simulations of a thorax phantom were performed showing the efficacy of this technique and the ability of SS-IGCT to suppress cone-beam artifacts compared to conventional CBCT. The noise and resolution characteristics are comparable to that of CBCT.