Two-dimensional molybdenum disulfide (MoS2) has been proven to be a candidate in photodetectors, and MoS2/lead sulfide (PbS) quantum dots (QDs) heterostructure has been used to expand the optical response wavelength of MoS2. Time-resolved pump-probe transient absorption measurements are performed to clarify the carrier transfer dynamics in the MoS2/PbS heterostructure. By comparing the carrier dynamics in MoS2 and MoS2/PbS under different pump wavelengths, we found that the excited electrons in PbS QDs can transfer rapidly (<100 fs) to MoS2, inducing its optical response in the near-infrared region, although the pump light energy is lower than the bandgap of MoS2. Besides, interfacial excitons can be formed in the heterostructure, prolonging the lifetime of the excited carriers, which could be beneficial for the extraction of the carriers in devices.