Corner pumping is a new pumping scheme for diode-pumped solid-state lasers, which has the advantages of high pump efficiency and favorable pump uniformity. A continuous-wave corner-pumped Nd:YAG/ YAG composite slab multi-wavelength laser at around 1.1 µm is demonstrated. The maximal output power is up to 12.06 W with an optical-to-optical conversion efficiency of 24%. At an output power of 10.3 W, the M(2) factors of beam quality at width and thickness directions are 7.71 and 2.44, respectively. With a LBO crystal inserted in the cavity, continuous-wave yellow-green laser with an output power of 841 mW is obtained. The experimental results show that a corner-pumping is a feasible scheme in the design of diode-pumped solid-state 1.1 µm lasers and their frequency-doubling to the yellow-green with low or medium output powers.