A semiconductor memory device of an embodiment includes: a semiconductor layer extending in a first direction; a first gate electrode layer; a second gate electrode layer provided apart from the first gate electrode layer in the first direction; and a gate insulating layer containing oxygen and at least one metal element of hafnium or zirconium, the gate insulating layer including a first region between the first gate electrode layer and the semiconductor layer, a second region between the first gate electrode layer and the second gate electrode layer, and a third region between the second gate electrode layer and the semiconductor layer, the first region including a crystal of an orthorhombic crystal system or a trigonal crystal system as a main constituent substance, and a distance between the second region and the semiconductor layer being larger than a distance between the first region and the semiconductor layer.