In this paper, we demonstrate how laser photodetachment mass spectrometry (LPMS) can be used to selectively detect C-13(-) ions in the presence of C-12(-) ions in a low energy ion beam. An isotopically enriched beam of carbon ions consisting of equal amounts of C-13(-) and 12C- ions was extracted from an ion source. The ions interacted with a laser beam in a collinear geometry over a distance of 70 cm. Residual atoms produced in the photodetachment process were detected in a neutral particle detector placed downstream of the collinear interaction region. By making use of the Doppler effect we were able to selectively photodetach C-13(-) ions. The number of detected C-13 atoms was 13 times larger than the number of detected C-12 atoms. The population of the excited, weakly bound D-2 excited state of the C- ion was depleted by the use of a second laser. This significantly reduced the background accompanying the signal arising from the photodetachment of the S-4 ground state C- ion. Different applications of the LPMS method will be discussed in the paper.