According to geometric feature of spherical surface,the misalignment characteristics of single spherical refracting system when the refracting surface was tilted and decentered were analyzed.From the principle of ordered multiplication of matrix of on-axis element and matrix of decentered element,the strict matrix which described the misaligned single spherical refracting system were presented.With the relation between system diffraction integral and the misaligned matrix element,the diffraction integral of the misaligned system was derived.Based on the structure parameters of fractional Fourier transform of single spherical refracting system,the misaligned fractional Fourier transform was also obtained.The result can be used in numerical calculation and simulation of diffraction and fractional Fourier transform of input complex amplitude of misaligned single spherical refracting system.