We report the results of studies on the electronic state of the hole-doped Y-based pyrochlore iridate, (Y1-x-yCuxCay)2Ir2O7. We carried out the resistivity, Muon Spin Relaxation (μSR), X-ray Photoemission Spectroscopy (XPS) measurements and Density Functional Theory (DFT) calculations on the non-doped (x=y=0) and doped (x=0.05, y=0.15) systems. We found in the non-doped system that the magnetic ordering of Ir spins which was accompanied by the metal-insulator transition (MIT) occurred at around 157 K and disappeared in the doped system in which MIT seems to disappear or smeared out. We suggest from the current study that a quantum critical point which shows a change in the electronic ground state from insulating to metallic to exist between those two systems.