We demonstrate a continuous-wave self-Raman Nd:GdVO4 Laguerre-Gaussian (LG) mode laser based on different Raman shifts of 382 cm-1 and 882 cm-1 by shaping the pumping beam with the use of an axicon lens and a focusing lens. Selective generation of LG mode beams at 1108 nm or 1173 nm, or simultaneously 1108 nm and 1173 nm, was achieved by carefully adjusting the alignment of the laser cavity. The maximum Raman LG mode output powers at the wavelengths of 1108 nm (the first-Stokes emission of the 382 cm-1 Raman shift) and 1173 nm (the first-Stokes emission of the 882 cm-1 Raman shift) were measured to be 49.8 mW and 133.4 mW at the absorbed pump power of 5.69 W, respectively. The generated LG modes, formed via the incoherent superposition of two LG mode beams with positive and negative topological charges, carry zero orbital angular momentum. Such LG mode laser sources have the potential to fill in the wavelength gap of lasers in the visible and infrared regions.