The characteristics of the polarization coupling of two optical micro/nano-fibers (MNFs), which are placed close and parallel each other, were investigated by three dimension full vector beam propagation method (3-D FVBPM). The analytical results of the polarization coupling show that a polarization beam splitter (PBS) device can be constructed based on the coupling of two parallel and close MNFs. In order to optimize the polarization splitting performance of the device, the geometric parameters of the PBS, such as the diameter of optical MNFs and the gap between them were investigated through numerical stimulation. The optimal parameters are diameter of 0.9 μm, gap of 0.5 μm and length of approximately 218 μm respectively. Additionally, fabrication tolerances of each parameter for the polarization splitter PBS were also investigated. In the case of incident wavelength at 1550 nm, and the polarization extinction ratio of both output ports of PBS larger than 15 dB, the fabrication tolerances for bandwidth and overlapping length are 10 nm and , ±2μm , whereas approximately -3nm~2nm for tolerances in the diameter and gap.