Simultaneous tunable two-wavelength operation of the tunable dye laser pumped by SHG of a Nd:YAG pulsed repetitive Q-switched laser is described. R6G, R6G+R640 and R6G+LD473 mixture in methanol solution were studied. The proper choice of the beam splitter and the Brewster prism pre-expander grazing-incident grating cavity provided a wide tunable spectral range, low background ASE; polarized peak output power of the laser is about 40 kW and a spectral bandwidth is 0.22cm-1.