According to one embodiment, a semiconductor memory device having a ferroelectric film, includes a semiconductor substrate, a field effect transistor formed on the semiconductor substrate, an inter-layer insulating film formed on the field effect transistor and the semiconductor substrate, a plug constituted with a single-crystalline structure, the plug being formed in the inter-layer insulating film and being connected with a source or a drain of the field effect transistor, a lower electrode constituted with a single-crystalline structure formed on the plug, a ferroelectric film formed on the lower electrode an upper electrode formed on the ferroelectric film.