Stacking faults are an important class of crystal defects commonly observed in nanostructures of close packed crystal structures. They can bridge the transition between hexagonal wurtzite (WZ) and cubic zinc blende (ZB) phases, with the most known example represented by the "nanowire (NW) twinning superlattice". Understanding the formation mechanisms of stacking faults is crucial to better control them and thus enhance the capability of tailoring physical properties of nanomaterials through defect engineering. Here we provide a different perspective to the formation of stacking faults associated with the screw dislocation-driven growth mechanism of nanomaterials. With the use of NWs of WZ aluminum nitride (AlN) grown by a high-temperature nitridation method as the model system, dislocation-driven growth was first confirmed by transmission electron microscopy (TEM). Meanwhile numerous stacking faults and associated partial dislocations were also observed and identified to be the Type I stacking faults and the Frank partial dislocations, respectively, using high-resolution TEM. In contrast, AlN NWs obtained by rapid quenching after growth displayed no stacking faults or partial dislocations; instead many of them had voids that were associated with the dislocation-driven growth. On the basis of these observations, we suggest a formation mechanism of stacking faults that originate from dislocation voids during the cooling process in the syntheses. Similar stacking fault features were also observed in other NWs with WZ structure, such as cadmium sulfide (CdS) and zinc oxide (ZnO).