In this study, the influence of an aging treatment on the shape memory effect and martensitic transformation was investigated in an Fe–Mn–Al–Ni alloy by adding a small amount of Nb and C elements. Results show that the aging treatment can significantly improve the shape recovery rate of the alloy. In the bending test with 4% deformation, after aging at 200 °C for 1 h, the recovery rate increased from 20 to 45%, and it further increased to 51% after the two-step aging treatment at 800 and 200 °C. The high-temperature in situ X-ray diffraction and atomic force microscope were used to reveal the shape memory effect between room temperature and 400 °C in this alloy due to γ′→α transformation. The microstructure of aged specimens was investigated using transmission electron microscopy. With the extension of the aging time from 0.5 to 6 h, the size of NiAl precipitation gradually grew from 9 to 32 nm, and the distribution became more uniform. Meanwhile, the NbC particles were found in the two-step aging treatment alloy, which was the key to improving the shape memory effect.