We propose a method for reconstructing the distributed forward state-of-polarization (SOP) in single-mode fiber (SMF), to solve the problem of unpredictable blind box of SOP evolution in many applications such as fiber-optic parametric amplification system. By using polarization-sensitive optical frequency domain reflectometry (POFDR) and a quaternion-based model to describe polarization changes, our approach achieves high spatial resolution and precision. By an improved iterative fitting algorithm, the mean square error (MSE) of forward SOP reconstruction for approximately 100 consecutive measurement points was reduced to below 0.1%. This method enables visualization of SOP dynamics along the fiber, offering critical insights for polarization-dependent systems