Efficient coupling from the silicon waveguide to the GeSi layer is the key to success in the GeSi electro-absorption(EA) modulator based on evanescent coupling. A lateral taper in the upper GeSi layer has room for increasing the modulating efficiency and alleviating the sensitivity of the extinction ratio(ER) and insertion loss(IL) to the length of the active region. The light behavior and the effect of the taper are explored in detail using the beam propagation method(BPM). After optimization, the light can nearly be totally confined in the GeSi layer without any oscillation. The modulator with the designed taper can achieve low IL and high ER. Efficient coupling from the silicon waveguide to the GeSi layer is the key to success in the GeSi electro-absorption (EA) modulator based on evanescent coupling. A lateral taper in the upper GeSi layer has room for increasing the modulating efficiency and alleviating the sensitivity of The extinction ratio (ER) and insertion loss (IL) to the length of the active region. The light behavior and the effect of the taper are explored in detail using the beam propagation method (BPM). After optimization, the light can nearly be totally confined in the GeSi layer without any oscillation. The modulator with the designed taper can achieve low IL and high ER.