We　demonstrate　a　passively　Q-switched　Yb:LSO　laser　based　on　tungsten　disulphide　(WS2)　saturable　absorber　operating　at　1034　nm　and　1056　nm　simultaneously.　The　saturable　absorbers　were　fabricated　by　spin　coating　method.　With　low　speed,　the　WS2　nanoplatelets　embedded　in　polyvinyl　alcohol　could　be　coated　on　a　BK7　glass　substrate　coated　with　high-refractive-index　thin　polymer.　The　shortest　pulse　width　of　1.6　mu　s　with　a　repetition　rate　of　76.9　kHz　is　obtained.　As　the　pump　power　increases　to　9　W,　the　maximum　output　power　is　measured　to　be　250　mW,　corresponding　to　a　single　pulse　energy　of　3.25　mu　J.　To　the　best　of　our　knowledge,　this　is　the　first　time　to　obtain　dual-wavelength　Q-switched　solid-state　laser　using　few-layer　WS2　nanoplatelets.