A corner-pumped type is a new pumping type in the diode-pumped solid-state lasers, which has the advantages of high pump efficiency and favorable pump uniformity. Using the single corner-pumped type, an efficient corner-pumped Nd:YAG/YAG composite slab continuous-wave 946 nm laser is demonstrated in this paper. The compact plane-concave linear cavity configuration is adopted and the cavity length is only 20 mm. When the pumping power is 50 W, the maximal output power can reach as high as 5.29 W with an optical-to-optical conversion efficiency of 10.6% and a slope efficiency of 12%. This laser has a compact structure, simple tuning and low cost, which will have a broad application prospect.