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Aiming to achieve InAs quantum dots (QDs) with a long carrier lifetime, the effects of Sb component in cap layers on the band alignment of the InAs/GaAsSb QDs have been studied. InAs QDs with high density and uniformity have been grown by molecular beam epitaxy. With increasing Sb composition, the InAs/GaAsSb QDs exhibit a significant red-shift and broadening photoluminescence (PL). With a high Sb component of 22％, the longest wavelength emission of the InAs/GaAs0.78Sb0.22 QDs occurs at 1.5 μm at room temperature. The power-dependence PL measurements indicate that with a low Sb component of 14％, the InAs/GaAs0.86Sb0.14 QDs have a type-I and a type-II carrier recombination processes, respectively. With a high Sb component of 22％, the InAs/GaAs0.78Sb0.22 QDs have a pure type-II band alignment, with three type-II carrier recombination processes. Extracted from time-resolved PL decay traces, the carrier lifetime of the InAs/GaAs0.78Sb0.22 QDs reaches 16.86 ns, which is much longer than that of the InAs/GaAs0.86Sb0.14 QDs (2.07 ns). These results obtained here are meaningful to realize high conversion efficiency intermediate-band QD solar cells and other opto-electronic device.