The potential energy curves and spectroscopic constants of the ground and 32 low-lying electronic states of ZrC have been studied by employing multireference configuration interaction methods, in conjunction with relativistic effective core potentials and 5s3p3d1f, 3s3p1d basis sets con Zr and C, respectively. We have determined that the ground state is (3)Sigma(+). However there are two low-lying (1)Sigma(+) states (below 5000 cm(-1)) which strongly interact resulting in avoided crossings. The lowest (1)Sigma(+) state corresponds to a combination of 1sigma(2) Xsigma(2) 1pi(4) configurations whereas the second is an open shell singlet 1sigma(2) 2sigma(1) 3sigma(1) 1pi(4). Several avoided crossings were observed, for (1)Pi, (3)Pi, (1)Delta, (3)Sigma(+), and (3)Delta states. We have identified (3)Pi and (1)Pi lying at 4367 and 5797 cm(-1), respectively. The results are in good agreement with the recent experimental findings of Rixon et al. [J. Mol. Spectrosc. 228, 554 (2004)], and indicate that the (3)Pi-(3)Sigma(+), and (1)Pi-(1)Sigma(+), bands located between 16 000-19 000 cm(-1) are extremely complex due to near degeneracy of several (1)Pi and (3)Pi states. We also have identified a (1)Sigma(+) state in the same region that may interfere with the (1)Pi emission bands. The present results not only shed further light into the spectra of ZrC but also predict yet to be observed systems.