Silicon photonics technology is a promising platform for photonics devices and system integration. However, due to the time-reversal symmetry, realizing silicon integrated isolators is still challenging. In this letter, an optical isolator based on the four-wave-mixing effect on silicon photonic integrated circuit platform is proposed and experimentally demonstrated. Different from typical nonlinear optical effect-based silicon integrated isolators, which can only be operated in either forward or backward directions (but not both), the isolator proposed here can be operated in both forward and backward directions simultaneously. The fundamental dynamic reciprocity limitation is overcome by a non-reciprocal wavelength conversion and wavelength filtering methodology. The fabricated silicon integrated isolator demonstrates an isolation ratio of >11.3 dB, and a 3-dB operational bandwidth exceeding 300 GHz. The insertion loss is < 19 dB and it can be further reduced by using higher pump power and optimizing linear loss. The isolation ratio can be enhanced as well by cascading filters.