Silicon electro-optical modulators based on add-drop micro-ring resonators have the advantage of more freedom in designing high-extinction-ratio and large-bandwidth modulators without changing the ion doping processes of the chip. Here we design a high-speed silicon modulator based on an add-drop micro-ring resonator with a radius of 20 m; it demonstrates high extinction ratio with low reverse bias. How the coupling between the straight waveguide and the ring resonator affects the performances is studied theoretically and it is found that a lower coupling coefficient at drop port leads to a higher extinction ratio but not the best bandwidth. Therefore, a balance should be considered between extinction ratio and bandwidth. According to the optimized result of the parameters the device is fabricated and tested. The spectrum testing indicates that the device can have 12 dB extinction ratio when it is operated at 3 V reverse bias. Furthermore, we have observed 8 Gbps open-eye diagram with only 1.2 V peak-to-peak signal voltage.