We present a novel high-repetition-rate photoelectron imaging (PEI) apparatus for exploring electronic structures of metal cluster anions. A continuous beam of mass-selected metal cluster anions, generated by a magnetron-sputtering cluster-ion source coupled with a quadrupole mass filter, is chopped into sub-megahertz ion bunches using a high-voltage pulser. The quasi-continuous anion beam is introduced into a PEI spectrometer, where the anions are photodetached using a 404nm (3.07eV) continuous-wave laser diode. As a demonstration, we acquire photoelectron images for size-selected Ag cluster anions, AgN - (N = 3, 7, 14), and show that each image can be obtained in a short accumulation time (50s) with a kinetic energy resolution (ΔE/E) of 4% at E = 1.77eV. The quasi-continuous PEI technique enables high-count-rate, space-charge-free acquisition of photoelectron spectra and angular distributions not only from size-selected metal cluster anions but also from anions prepared by other continuous ion sources, such as electrospray ionization.