Based on an analysis of the surface admittance of a plasmonic film with a substrate, we propose an ultrathin quarter-wave plate consisting of a periodic plane array of symmetrical L-shaped plasmonic antennas. The period, which determines the coupling among L-shaped antennas, is an important parameter for optimizing the performance of the structure. Numerical simulation results show that an Au quarter-wave plate designed in this Letter can efficiently convert a linearly polarized light at normal incidence into circularly polarized light, whose ellipticity is 0.994 at an operating wavelength of 1550 nm. The thickness is only 30 nm, which is nearly 1/50 of the wavelength of incident light.