Carrier dynamics of InAsGaAs quantum dots (QDs) covered by a thin Ga As1-x Sbx layer were investigated by time-resolved photoluminescence (PL). Both the power dependence of PL peak shift and the long decay time constants confirm the type-II band alignment at the GaAsSb-InAs interface. Different recombination paths have been clarified by temperature dependent measurements. At lower temperatures, the long-range recombination between the QD electrons and the holes trapped by localized states in the GaAsSb layer is important, resulting in a non-single-exponential decay. At higher temperatures, optical transitions are dominated by the short-range recombination with the holes confined to the band-bending region surrounding the QDs.