We present an experimental and theoretical study of the optically detected magnetic resonance signals for ensembles of negatively charged nitrogen-vacancy (NV) centers in a C13 isotopically enriched single-crystal diamond. We observe four broad transition peaks with superimposed sharp features at zero magnetic field and study their dependence on an applied magnetic field. A theoretical model that reproduces all qualitative features of these spectra is developed. Understanding the magnetic-resonance spectra of NV centers in an isotopically enriched diamond is important for emerging applications in nuclear magnetic resonance.