Resistivity, thermal diffusivity, lattice and magnetic properties of double perovskite Sr2-xLaxMnMoO6 are investigated with systematic change of La doping concentration x from 0.0 to 0.4. The insulator to metal phase transition is observed with increasing x above 0.3, suggesting that the extra electrons via substitution of La3+for Sr2+ ions occupy mainly the conduction Mo-4d band. According to the insulator to metal phase transition,the thermal diffusivity of Sr2-xLaxMnMoO6 enhances from 0.33cm2/s at x = 0.0 to 0.49cm2/s at x = 0.4. We further investigate the La doping effects on the lattice and magnetic properties.