Current computed tomography (CT) scanners, including micro‐CT scanners, utilize a point x‐ray source. As we target higher and higher spatial resolutions, the reduced x‐ray focal spot size limits the temporal and contrast resolutions achievable. To overcome this limitation, in this paper we propose to use a line‐shaped x‐ray source so that many more photons can be generated, given a data acquisition interval. In reference to the simultaneous algebraic reconstruction technique (SART) algorithm for image reconstruction from projection data generated by an x‐ray point source, here we develop a generalized SART algorithm for image reconstruction from projection data generated by an x‐ray line source. Our numerical simulation results demonstrate the feasibility of our novel line‐source based x‐ray CT approach and the proposed generalized SART algorithm.