A method for fabricating a capacitor of a semiconductor device, includes the steps of: forming a first insulating layer and then a second insulating layer on the first insulating layer; removing the second insulating layer of a first electrode region of a capacitor; forming a side wall at a side of the second insulating layer; etching the first insulating layer by using the side wall of the second insulating layer as a mask so as to form a contact hole; forming a first electrode of a capacitor on the side wall and on the contact hole; forming a dielectric layer on the first electrode of the capacitor; and forming a second electrode of the capacitor on the dielectric layer. And, a capacitor in a semiconductor device includes: a substrate; a first insulating layer being formed at an upper part of the substrate 20 and having a contact hole; a second insulating layer being formed at an upper part of the first insulating layer; side walls being formed at an upper part of the first insulating layer and at a side surface of the second insulating layer both in an arc-shape; a first electrode of a capacitor being formed on the contact hole and the side walls; a dielectric layer formed on the first electrode of the capacitor; and a second electrode of the capacitor being formed on the first electrode of the capacitor.