We demonstrate a photonic band gap (PBG) from one-dimensional (1D) periodic structures created by a double-layer unit cell with an air layer and an anisotropic nonmagnetic left-handed metamaterial (LHM) layer whose permittivity elements are partially negative. The requirements imposed on the materials and structures to realize a PBG are derived when the frequency is above or below the cutoff frequency, and the transmission properties of the PBG are discussed by utilizing 4×4 transfer-matrix method with dispersive semiconductor metamaterial.