Iterative maximum likelihood (ML) transmission computed tomography algorithms have distinct advantages over Fourier-based reconstruction, but unfortunately require increased computation time. The convex algorithm [1] is a relatively fast iterative ML algorithm but it is nevertheless too slow for many applications. Therefore, an acceleration of this algorithm by using ordered subsets of projections is proposed [ordered subsets convex algorithm (OSC)]. OSC applies the convex algorithm sequentially to subsets of projections. OSC was compared with the convex algorithm using simulated and physical thorax phantom data. Reconstructions were performed for OSC using eight and 16 subsets (eight and four projections/subset, respectively). Global errors, image noise, contrast recovery, and likelihood increase were calculated. Results show that OSC is faster than the convex algorithm, the amount of acceleration being approximately proportional to the number of subsets in OSC, and it causes only a slight increase of noise and global errors in the reconstructions. Images and image profiles of the reconstructions were in good agreement. In conclusion, OSC and the convex algorithm result in similar image quality but OSC is more than an order of magnitude faster.