Lead-free halide double perovskites (DPs) have attracted great attention due to their stability, nontoxicity and good photophysical property. In this work, we report a new, small-bandgap Cs2CuSbCl6 DP nanocrystals (NCs) with a bandgap of 1.66 eV, which is the smallest bandgap in reported lead-free three-dimensional DP NCs. Density functional theory calculations confirm that Cs2CuSbCl6 DP has an indirect bandgap of 1.70 eV, in good agreement with the experimental result. The photophysical property of Cs2CuSbCl6 NCs is studied by the combination of femtosecond transient absorption (TA) and nanosecond TA techniques. In addition, the Cs2CuSbCl6 NCs exhibit good stability exposed in the air. These results show that these NCs will have great potential to be used as a light-absorbing material for photovoltaic applications.