Time-resolved photoluminescence (PL) of sub-monolayer (SML) InGaAs/GaAs quantum-dot-quantum-well heterostructures was measured at 5 K for the first time. The radiative lifetime of SML quantum dots (QDs) increases from 500 ps to 800 ps with the increase of the size of QDs, which is related to the small confinement energy of the excitons inside SML QDs and the exciton transfer from smaller QDs to l arger ones through tunneling. The rise time of quantum-dot state PL signal stron gly depends on the excitation power density. At low excitation power density, th e rise time is about 35 ps, the mechanism of carrier capture is dominated by the emission of longitudinal-optical phonons. At high excitation power density, the rise time decreases as the excitation density increases, and Auger process pla ys an important role in the carrier capture. These results are very useful for u nderstanding the working properties of sub-monolayer quantum-dot devices.