A low loss, small crosstalk offset crossing structure for a Si wire waveguide is proposed. We analyzed the properties of the structure for both the TE and TM modes by 2-D FDTD (two-dimensional finite difference time domain) simulation. By optimizing the offset crossing structure, a transmission loss of 0.021dB, and crosstalk of -55.0dB was achieved with a crossing angle of 20 degrees for the TE mode. A transmission loss of 0.070dB, and crosstalk of -48.6dB was also achieved with the same crossing angle for the TM mode. The low losses achieved with a small crossing angle makes this structure very useful for highly integrated optical matrix switches, etc.