Laser ion sources are expected to be used in various applications of heavy ion beam technology. The plasma direct injection scheme (DPIS) is a method in which ion beams extracted from a laser ion source are directly injected into a radio frequency quadrupole (RFQ) linear accelerator. In this study, a new shape of the plasma electrode with a concave surface for the DPIS was proposed to inject a converging beam to a cavity of RFQ accelerator. This approach allows the use of a large-diameter extraction electrode, which is not limited by the aperture of the RFQ electrode rods. The DPIS, using the concave surface electrode, was employed to accelerate C6+ ion beams. The results indicated that both the beam current and the number of ions increased nearly twice with the proposed electrode shape compared to values obtained with the conventional electrode. This enhancement corresponded to the increased extraction area of the beam.