Single crystals of LaIrSi3 and CeIrSi3 were grown by the Czochralski pulling method in a tetra-arc furnace and the magnetic and superconducting properties, together with superconductivity in CeIr1-xCoxSi3, were clarified by measuring the electrical resistivity, specific heat, magnetic susceptibility, magnetization and de Haas-van Alphen (dHvA) effect. From the results of the dHvA experiment for LaIrSi3, the Fermi surface is found to split into two Fermi surfaces due to the spin-orbit interaction arising from the non-centrosymmetric crystal structure, which are separated by about 1000K. Similar split Fermi surfaces are expected in the antiferromagnet CeIrSi3. The electronic state of CeIrSi3 is tuned from the anti ferromagnetic state to the superconducting state by applying pressure. The upper critical field H-c2(0) at a pressure of 2.65 GPa is found to be highly anisotropic: H-c2(0) = 95 kOe for H vertical bar vertical bar [110] and H-c2(0) similar or equal to 300 kOe for H vertical bar vertical bar [001], with the superconducting transition temperature T-sc similar or equal to 1.6 K. The large magnitude and anisotropy of H-c2(0) in CeIrSi3 are consistent with the theoretical prediction for superconductivity in the non-centrosymmetric crystal structure. Superconductivity is also observed at ambient pressure in CeIr1-xCoxSi3.