We report a double Q-switched 946 nm laser with a magnesium-oxide-doped LiNbO3 (MgO:LN) electro-optic (EO) crystal and a monolayer molybdenum diselenide (MoSe2) saturable absorber (SA). A pulsed laser diode side-pumped long neodymium-doped yttrium aluminum garnet rod (φ3×65 mm) is used as the gain medium. Large pulse energy up to 3.15 mJ and peak power up to 346 kW are generated at the repetition rate of 550 Hz, corresponding to the beam quality factors of Mx2=3.849, My2=3.868. Monolayer MoSe2 nanosheets applied in the experiment would be a promising SA for a passive Q-switching operation.