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. A corner-pumped Nd:YAG/YAG composite slab continuous-wave 1319 nm/1338 nm dual-wavelength laser is first demonstrated in this paper. When the cavity length is 25 mm, the maximal output power is up to 7.62 W with a slope efficiency of 16.6% and an optical-to-optical conversion efficiency of 17%. The corresponding spectral line widths of 1319 nm laser and 1338 nm laser are 0.11 and 0.1 nm, respectively. The short-term instability of the output power is better than 1% when the pumping power is 39.5 W. The experimental results show that a corner-pumped type is a kind of feasible schedules in the design of diode-pumped solid-state 1.3 μm lasers with low or medium output powers.