Variable-spun fiber wave plate can be used to change the polarization state in fiber optic sensing systems. However, the beat length of the birefringence fiber may variation with different operating wavelength, which further leads to the instability of the polarization transforming performance. Based on the relation between the beat length and the operating wavelength, the wavelength sensitivity is simulated for the variable-spun fiber wave plate with different structural parameters (fiber length, spun rate profile and maximum spun rate). The achromatic bandwidth of the qualified fiber plate is discussed. The results have certain reference value for the design, fabrication and evaluation of variable-spun fiber wave plate.