In this paper, highly efficient TE0-TE1 and TM0-TE1 conversions are achieved on SOI chips by optimizing the edge of mode converters employing the adjoint shape optimization method. At the central wavelength of 1550 nm, the conversion efficiencies of the device reaches 99.6% for TE0-TE1 conversion and 96.0% for TM0-TE1 conversion, while the loss are only 0.016 dB and 0.17 dB, respectively. Besides, the extinction ratio reaches 31.2 dB and 29.5 dB. The bandwidth characteristics of the devices are also numerically investigated. As the wavelength varies from 1500 nm to 1600 nm, the conversion efficiency for TE0-TE1 conversion can be kept above 96.6% and the extinction ratio is kept above 15.7 dB, while the insertion loss is kept below 0.14 dB. As for TM0-TE1 conversion, the conversion efficiency is above 92.6%, the extinction ratio is over 15.6 dB and insertion loss is below 0.33 dB within the wavelength range from 1505 nm to 1585 nm. Considering the influence of fabrication process on the performance of devices, the fabrication tolerance of mode converters is investigated by adjusting the width of devices. For both converters, the conversion efficiencies can be kept above 91.9%, while the insertion loss is less than 0.34 dB as the width variation of ± 20 nm at 1550 nm. The proposed mode converters take advantages of large bandwidth, high conversion efficiencies, low insertion loss and high fabrication tolerance, paving the path to realize efficient on-chip mode conversion in a cost-effective way.