We search for the dark photon cold dark matter (DP-CDM) using a cryogenic millimeter-wave receiver. DP-CDM weakly couples to electromagnetic fields with a coupling constant of χ, and is converted into ordinary photons at the surface of a metal plate. We search for signal of this conversion in the frequency range 18--26.5GHz, which corresponds to the mass range 74--110μeV/c2. We found no signal, allowing us to set an upper bound of χ<(0.3--2.0)×10−10 at 95% confidence level. This is the most stringent constraint to date, and tighter than that set by cosmological observations.