Ferroelectricity in ultrathin two-dimensional (2D) materials has attracted broad interest due to potential applications in nonvolatile memory, nanoelectronics and optoelectronics. However, ferroelectricity is barely explored in materials with native centro or mirror symmetry, especially in the 2D limit. Here, we report the first experimental realization of room-temperature ferroelectricity in van der Waals layered GaSe down to monolayer with mirror symmetric structures, which exhibits strong intercorrelated out-of-plane and in-plane electric polarization. The origin of ferroelectricity in GaSe comes from intralayer sliding of the Se atomic sublayers, which breaks the local structural mirror symmetry and forms dipole moment alignment. Ferroelectric switching is demonstrated in nano devices fabricated with GaSe nanoflakes, which exhibit exotic nonvolatile memory behavior with a high channel current on/off ratio. Our work reveals that intralayer sliding is a new approach to generate ferroelectricity within mirror symmetric monolayer, and offers great opportunity for novel nonvolatile memory devices and optoelectronics applications.