We demonstrate the hybrid silicon and electro-optic (EO) polymer modulator for low-driving voltage and high bandwidth applications. The designed hybrid waveguide was fabricated by the conventional photolithography technique, so that this widespread compatibility enabled the construction of the unique polymer photonic devices. The waveguide consists of the silicon core with a 50 nm-thick and 2 m-wide core and the EO polymer cladding. The optical mode calculation indicates that the large extension of the optical field into the EO polymer provides the EO coefficient of about 80 pm/V in the waveguide. Therefore, the half-wave voltage of the hybrid waveguide was recorded only 1.1 V at 1550 nm in the Mach-Zehnder modulator. The measured insertion loss was about 15 dB, which included the materials absorption loss of the EO polymer. The traveling-wave-electrodes were applied to the hybrid waveguide in order to evaluate the frequency response of the modulator up to 40 GHz by measuring the S21 parameter. The -3 dB bandwidth of 20 GHz and a 6 dB reduction in response at 40 GHz were measured. This bandwidth is mainly limited by the conductor loss of the electrode, which can be improved further by the fabrication. The hybrid waveguide showed the excellent temperature stability at 85C for longer than 2000 hours.