Solar-pumped lasers have promising potential in space technology. The first solar-pumped 1061-/1064-nm dual-wavelength Nd:YAG monolithic laser is proposed. The resonant cavity of the laser is formed by coating the dielectric film directly on both ends of the laser medium, and the thin film coated on the output end is specially designed to adjust the transmittance at 1061 and 1064 nm, thus balancing the threshold pump power and realizing a dual-wavelength output. Through theoretical analyses and simulations, a solar-pumped 1061-/1064-nm dual-wavelength laser with improved output power of 81.3 mW was achieved, corresponding to the slope efficiency of 0.13% and the optical-to-optical efficiency of 0.085%, which provides a possible solution for dual-channel space laser communication.