A high-performance lead sulfide (PbS) NCs/ graphene hetero-junction based phototransistor was reported. The device exhibited NIR response with a responsivity of 33 A/W, detectivity of $2.2\times 10 ^{8}$ Jones, external quantum efficiency of $5\times 10 ^{3}$ % and fast response time of 16 ms at 808 nm under room temperature. In addition, the phototransistor exhibited good memory function by introducing graphene oxide storage layer. The mechanism of the device has been discussed using the energy band diagrams of the hetero-structured PbS NCs/graphene.