The dynamic equations which describe the pulse nonlinear polarization rotation (NPR) of nonlinear birefringence in ring cavity fiber laser were given. The theoretical formulae of spectrum sideband offset which stems from the interference between the dispersion wave and the soliton wave are deduced in ring cavity fiber laser passively mode-locked by the nonlinear polarization rotation technique. Theoretical spectral sideband offsets are consistent with experimental results very well in the paper. And the maximal error is less than 4.1%, which explains the sideband offset in ring cavity fiber laser under passive mode-locking by NPR.