Partial volume (PV) effects degrade the quantitative accuracy of SPECT brain images. In this paper, we extended a PV compensation (PVC) method originally developed for brain PET, the geometric transfer matrix (GTM) method, to brain SPECT using iterative reconstruction-based compensations. In the GTM method a linear transform between the true regional activities and the measured results was assumed. Elements of the GTM were calculated by projecting and reconstructing maps with uniform regions representing different structures. However, with iterative reconstruction methods, especially when reconstruction-based compensation for detector response was applied, we found that it was important to treat the region maps as a perturbation to the reconstructed image in the estimation of the GTM. This modified method, termed perturbation-based GTM (pGTM) was evaluated using Monte Carlo (MC) simulated and experimentally acquired data. Results showed great improvement of the quantitative accuracy in brain SPECT imaging. For MC simulated data, PVC using pGTM reduced the underestimation of striatal activities from 30% to less than 1.2%. For experimental data, PVC using pGTM reduced the underestimation of striatal activities from 36% to less than 7.8%. The underestimation of the striatum to background activity ratio was also improved from 31% to 2.7%.