N-type 4H-SiC crystals were grown by the physical vapor transport (PVT) method with nitrogen and aluminum (N-Al) co-doping. By using aluminum carbide powder preannealed in nitrogen gas atmosphere as an aluminum doping source, we obtained highly N-Al co-doped crystals with a nitrogen concentration higher than that in nitrogen-only-doped crystals. The dislocation densities of N-Al co-doped crystals with a high aluminum concentration (> 1 x 10(19) cm(-3)) were found to become higher than those with a low aluminum concentration (< 1 x 10(19) cm(-3)). Moreover, we investigated the expansion velocities of double Shockley-type stacking faults (DSFs) in the N-Al co-doped and the nitrogen-only-doped crystals. We found that the DSF expansion velocities in the N-Al co-doped crystals were lower than those in the nitrogen-only-doped crystals. This difference in the DSF expansion velocity is discussed with respect to the quantum well action model.