The authors have derived a filtered-backprojection (FBP) reconstruction algorithm for fan-beam SPECT that eliminates artifacts associated with patient motion during brain imaging. It is assumed that the patient motion is known or can be measured separately, and that the head is rigid. The in-plane translation and relation were studied and were incorporated into the proposed FBP reconstruction algorithm. Angular-dependent translation/rotation parameters were used to correct for multiple motions that could occur during a scan. The proposed FBP reconstruction algorithm was evaluated using Monte Carlo simulated phantom data, including a two-point-source phantom and the Hoffman brain phantom. Projections with translation, rotation and their combinations were generated, and images reconstructed using the proposed algorithm and the standard FBP algorithm were compared. Artifacts were observed in images without the motion correction, but the artifacts were eliminated or greatly reduced using the proposed reconstruction algorithm.