The superconducting ground state of recently discovered ZrIrSi is probed by means of muon spin rotation and relaxation (mu SR) and resistivity measurements. The occurrence of superconductivity at T-C = 1.7 K is confirmed by resistivity measurements. Zero field mu SR study revealed that below T-C there is no spontaneous magnetic field in the superconducting state, which indicates time-reversal symmetry is preserved in the case of ZrIrSi. From transverse field mu SR measurement, we have estimated the superfluid density as a function of temperature, which is described by an isotropic s-wave model with a superconducting gap 2 Delta(0)/k(B)T(C) = 5.10(2) and indicates the presence of strong coupling superconductivity. Ab initio electronic structure calculation indicates that there are four bands passing through the Fermi level, forming four Fermi surface pockets. We find that the low-energy bands are dominated by the 4d orbitals of the transition metal Zr, with substantially less weight from the 5d orbitals of the Ir atoms.