It is known that few Co-based superconducting compounds have been found compared with their Fe- or Ni-based counterparts. In this study, we have found superconductivity of 4 K in the LaCoSi compound for the first time. The combined analysis of neutron and synchrotron X-ray powder diffractions reveals that LaCoSi exhibits an isostructure with the known Fe-based LiFeAs superconductor, which is the first "111" Co-based superconductor. First-principles calculation shows that LaCoSi presents a quasi-two-dimensional band structure that is also similar to that of LiFeAs. The small structural distortion may be more conducive to the emergence of superconductivity in the LaCoSi compound, which provides a direction for finding new Co-based superconducting compounds.