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We report observations of a strong thickness dependence for charge transfer (CT) from MoSe2 to MoS2, as evidenced by transient absorption measurements. By time-resolving CT from MoSe2 monolayers (1Ls) to MoS2 flakes of varying thicknesses, including 1L, bilayer (2L), and trilayer (3L), we find that the CT time is several picoseconds in the 1L-MoSe2/3L-MoS2 heterostructure, which is much longer than that of 1L-MoSe2/1L-MoS2 and 1L-MoSe2/2L-MoS2 heterostructures. In addition, the recombination lifetime of the interlayer excitons in the 1L/3L heterostructure is several times longer than that of 1L/1L and 1L/2L heterostructures, reaching 800 ps. Furthermore, we show that a prepulse can reduce the CT time and enhance the interlayer exciton recombination in the 1L/3L heterostructure. These findings illustrate that layer thickness can be an important parameter to control the CT property of van der Waals heterostructures. These experimental results also provide important information for further refining the understanding of the physical mechanisms of CT in van der Waals heterostructures.