Cubic phase CsPbI3 quantum dots (alpha-CsPbI3 QDs) as a newly emerging type of semiconducting QDs hold tremendous promise for fundamental research and optoelectronic device applications. However, stable and sub-S nm-sized alpha-CsPb(I)3 QDs have rarely been demonstrated so far due to their highly labile ionic structure and low phase stability. Here, we report a novel strontium-substitution along with iodide passivation strategy to stabilize the cubic phase of CsPbI3, achieving the facile synthesis of alpha-CsPbI3 QDs with a series of controllable sizes down to sub-5 nm. We demonstrate that the incorporation of strontium ions can significantly increase the formation energies of alpha-CsPbI3 QDs and hence reduce the structure distortion to stabilize the cubic phase at the few-nanometer size. The size ranging from 15 down to sub-5 nm of as-prepared stable alpha-CsPbI3 QDs allowed us to investigate their unique size-dependent optical properties. Strikingly, the few-nanometer-sized alpha-CsPbI3 QDs turned out to retain high photoluminescence and highly close packing in solid state thin films, and the fabricated red light emitting diodes exhibited high brightness (1250 cd m(-2) at 9.2 V) and good operational stability (L-50 > 2 h driven by 6 V). The developed cation-substitution strategy will provide an alternative method to prepare uniform and finely size-controlled colloidal lead halide perovskite QDs for various optoelectronic applications.