The charge-carrier dynamics of lead-free halide double-perovskite Cs2AgBi1−xSbxBr6 (0 ≤ x ≤ 0.75) nanocrystals (NCs) are studied by using femtosecond transient absorption technique. The ground-state bleaching decay signal can be fitted by using a triple-exponential function with lifetimes of τ1 = 0.8 ps (ultrafast component), τ2 = 64.4 ps (fast component), and τ3 = 4.3 ns (slow component) in Cs2AgBiBr6 NCs. Pump-fluence dependent TA spectra indicate that the ultrafast and fast component account for the majority of the total decay process and which can be assigned to the charge-carrier trapping processes. The slow component is due to the exciton geminate recombination because of the large exciton binding energy. Furthermore, we find that the charge-carrier trapping processes account for larger proportion with higher Sb content in Cs2AgBi1−xSbxBr6 NCs, which may be due to the increased carrier-phonon coupling strength with Sb incorporating. Besides, we find the absorption cross-section decreases with increasing Sb content. The in-depth understanding of the charge-carrier dynamics is beneficial for further developing lead-free double-perovskite NCs with improved optoelectronic properties.