Passively Q-switching of dual-wavelength lasers at 1064 nm and 1342 nm is realized in a laser doide (LD) end-pumped three-mirror compound resonator Nd:YVO4 laser using graphene dispersion as the saturable absorber, by setting the cavity lengths and the output mirror transmissivities of two branch cavity appropriatly. When the transmissivity of 1064 nm branch cavity is 20%, both 1064 nm pulse with 10.8 ns duration and 1342 nm pulse with 12.5 ns duration are achieved, and the 1064 nm pulse is in the front, the time interval between two pulses is 16 ns. Both 1064nm pulse with 11.3 ns duration and 1342 nm pulse with 14.2 ns duration are achieved when the transmissivity of 1064 nm branch cavity is 25%, and 1342 nm pulse is in the front, the time interval between two pulses is 19 ns. A reasonable theoretical explanation is given to the above-mentioned experiment according to dual-wavelength line competition and the saturable absorption of grephene in 1064 nm and 1342 nm lasers.