We present a pumping scheme for a quasi-three-level solid-state laser. The scheme uses a slab laser configuration with the pump light incident from the slab corners. A diode-corner-pumped composite Yb:YAG-YAG slab laser operating in high-power cw mode was designed to prove the scheme. As much as 520 W of output power was obtained from a single 1-mm-thick composite slab with 0.5-at. %-doped Yb:YAG. The slope efficiency and the optical-to-optical efficiency with respect to the pump power were 32% and 25%, respectively. This result shows the validity of the corner-pumping concept and its feasibility in the development of high-power solid-state lasers.