A fast-axis-adjustable photoelastic modulator (Faa-PEM) is developed and studied, and a spectropolarimetric imaging method using the Faa-PEM and an acousto-optic tunable filter is presented. The Faa-PEM modulation retardation amplitude and fast-axis direction of the Faa-PEM can be adjusted by adjusting the two drives with no mechanical rotation. The I, Q, and U of the Stokes parameters of the incident light can be obtained by adjusting the retardation amplitude and fast-axis direction of the Faa-PEM. This measurement method does not require high-frequency components, and thus a general area array detector can realize the measurement. Theoretical simulation analyses show that the relative errors ΔI/I, ΔQ/Q, ΔU/U, and ΔDoLP/DoLP are less than 5.6% and that the deviation error ΔAoLP is less than 0.2° (at I=1.00, Q=0.707, U=0.707, V=0.0, -0.1°≤Δθ0≤0.1°, and -0.05 rad≤Δδ0≤0.05 rad). A prototype was developed and tested. The test results show that the average absolute relative error of the degree of linear polarization is 0.36%, and the average absolute deviation error of the angle of linear polarization is 0.048°. The method has potential application value in spectropolarimetric imaging technology.