In this paper, a compact, broadband, and CMOS compatible ${2} \times {2}$2×2 optical switch based on hybrid plasmonic waveguides (HPWs) and curved directional coupler is presented. The proposed coupler consists of a combination of straight and curved hybrid plasmonic waveguides. By using the ability of HPWs for confining the light wave in a sub-wavelength scale and the curved structure to decrease the wavelength dependence of the directional coupler, a 3 dB power splitter with a ${3}\,\,\textrm{dB} \pm 0.5$3dB±0.5 bandwidth of about 410 nm and a footprint of ${7.6}\,\,\unicode{x00B5}\textrm{m} \times {2}\,\,\unicode{x00B5}\textrm{m}$7.6µm×2µm is achieved. By exploiting this optimal power splitter in a Mach-Zehnder interferometer structure, a ${2} \times {2}$2×2 electro-optic switch with a broad bandwidth of 400 nm and a small footprint of ${33}\,\,\unicode{x00B5}\textrm{m} \times {2.5}\,\,\unicode{x00B5}\textrm{m}$33µm×2.5µm is realized, which denotes the widest bandwidth compared to the previously reported similar structures. The three-dimensional finite-difference time-domain simulation results show a switching speed of 0.15 THz for the proposed optical switch, while the extinction ratio, power consumption, and insertion loss are 20 dB, 95.2 fJ/bit, and 4 dB, respectively, at the central wavelength of 1550 nm.