Asymmetric Y-branch waveguides are important passive components for unequal power splitting, and are widely used in integrated optical circuit. Based on total internal reflection, novel asymmetric Y-branch waveguide is proposed, in which there is little horizontal offset distance between the branch point of the two branch waveguides and the axe of the input waveguide, and the branching ratio can be controlled by changing offset distance. Its optical characteristic is thoroughly investigated by using finite difference beam propagation method(FD-BPM). The simulated results show that arbitrary branching ratio can be realized, and the optical power loss is only 0.417 dB while the branching angle is 14°. This novel asymmetric Y-branch waveguides with low polarization dependence can be easily fabricated, and have more advantages than previously designed ones while being used in integrated optical devices.