The newly discovered noncentrosymmetric superconductor ThCoC2 exhibits numerous types of unconventional behavior in the field dependent heat capacity data. Here we present the first measurement of the gap symmetry of ThCoC2 by muon spin rotation and relaxation (mu SR) measurements. The temperature dependence of the magnetic penetration depth measured using the transverse field mu SR experiment reveals the evidence of a nodal pairing symmetry. To understand this finding, we carry out calculations of the superconducting pairing eigenvalue and eigenfunction (pairing symmetry) due to the spin-fluctuation mechanism by directly implementing the ab initio band structures. We find that the system possesses a single Fermi surface with considerable three dimensionality and a strong nesting along the k(z) direction. Such nesting promotes a superconducting state with a cos k(z)-like pairing symmetry with a prominent nodal line on the k(z) = +/-pi/2 plane. The result agrees well with the experimental data.