The present invention relates to an electrospinning device for fabricating a membrane, in particular, to an electrospinning device for fabricating membrane by using spinnerets aligned in machine direction (MD) and transverse direction (TD) in a high-voltage DC electric field, and to method for using the same. In addition to producing a single-layer nanofiber membrane from a polymer composite, the electrospinning device according to the present invention can also conveniently produce a multilayer composite nanofiber membrane from more than one polymer composites. The electrospinning device comprises a control section, an electrospinning section and an ancillary section. The electrospinning section comprises a MD spinnerets set and a TD spinnerets set that are alternately arranged and moves above a membrane collecting device in a to-and-fro scanning manner so as to improve the evenness and strength of the obtained membrane. The high-voltage DC electric field is applied between the MD and TD spinnerets sets and a stainless steel conveyer belt for collecting the membrane. A polymer solution supplied to the MD and TD spinnerets sets is split into nanoflows under the action of the electric field, accumulated on the stainless steel conveyer belt to form a membrane and carried to a collecting roller to be collected.