A semiconductor device containing an MIM capacitor and its fabrication method are provided. A metal-insulator-metal (MIM) capacitor is formed on a first interlayer dielectric layer covering a substrate. The MIM capacitor includes a bottom electrode layer and a top electrode layer that are isolated from and laterally staggered with one another. A second interlayer dielectric layer is formed to cover both the MIM capacitor and the first interlayer dielectric layer. A first conductive plug and a second conductive plug are formed each passing through the second interlayer dielectric layer. The first conductive plug contacts a sidewall and a surface portion of the top electrode layer of the MIM capacitor and the second conductive plug contacts a sidewall and a surface portion of the bottom electrode layer of the MIM capacitor.