Photonic bandgaps (PBGs) in traditional one-dimensional (1-D) binary photonic crystals (PhCs) consisting of two kinds of isotropic dielectrics strongly shift towards shorter wavelengths as incident angle increases. Such blueshift property of PBGs intensively limits the widths of omnidirectional photonic bandgaps (OPBGs). Very recently, researchers achieved a special kind of PBGs called angle-insensitive PBGs in novel 1-D binary PhCs consisting of isotropic dielectric and elliptical metamaterial (EMM). The emergence of such angle-insensitive PBGs provides us an opportunity to achieve large OPBGs. Herein, we periodically introduce plasma layers into a 1-D binary PhC consisting of isotropic dielectric and EMM with an angle-insensitive PBG to achieve a large OPBG at mid-infrared wavelengths. The EMM is mimicked by an all-dielectric subwavelength multilayer. The broaden effect of the OPBG originates from the plasmonic property of plasma and the angle-insensitive property of the PBG. The width of the OPBG reaches 4.19 μm. Our work provides a feasible route to achieving large OPBGs in 1-D PhCs and would promote the development of OPBG-based devices, such as omnidirectional broadband reflectors and omnidirectional filters.