For Nd:LaxLu1−xVO4 (x = 0.05) crystal, the 4F3/2→4I13/2 transition property was investigated for the first time. The fluorescence peak of Nd:La0.05Lu0.95VO4 crystal exhibited inhomogeneous broadening comparing with that of Nd:LuVO4 crystal. With a laser diode array as the pump source, continuous-wave (CW) and active/passive Q-switched laser operation based on the 4F3/2→4I13/2 transition was realized. For CW laser operation, the maximum output powers of 0.561 and 0.718 W were obtained with slope efficiencies of 11.3% and 12.5% and optical-to-optical conversion efficiencies of 8.9% and 7.7%, respectively, for a and c cut crystal samples. For acousto-optic/passively Q-switched laser operation, the shortest pulse width, highest peak power and maximum pulse energy reached 44 ns, 273 W and 12 μJ, and 41 ns, 199 W and 8.2 μJ, respectively. Our research has indicated that Nd:LaxLu1−xVO4 is a promising gain medium for mode-locked laser operation at 1.34 μm.