The developments in polarized light have spawned a multitude of novel applications in optical fiber systems, but the design and fabrication of practical fiber wave plates with high degree of integration still remain a challenging issue. To address this problem, an all-fiber spun wave plate (SWP) for arbitrary state of polarization (SOP) conversion is proposed in this work, and its principle is analyzed with Mueller matrix. Simulations are conducted to exhibit the arbitrary SOP conversion capability of the proposed SWP, and two key parameters, including the maximum spinning rate (ξmax) and linear birefringence (δ), are investigated for efficient conversion of desired SOP. Different functions to increase the spinning rate ξ from 0 to ξmax, computational efficiency and accuracy related to N are discussed in detail. Furthermore, the depolarization effect caused by retardation of SWP is also considered. The results of this research suggest that the proposed SWP exhibits promising performance in arbitrary SOP conversion, and the meticulous analysis of the numerical computation, design, and implementation of SWP presented in this work can provide novel insights for devloping fiber wave plates.