To resolve fine details, or to accurately segment tumors from background activities, it is desired that the reconstruction image of the SPECT may preserve the edges and achieve high resolution. In this paper, we develop a blind deblurring reconstruction technique estimate of both the actual image and the PSF of the system, and enhance the performance of iterative reconstruction using this technique. A blurred SPECT reconstruction can be viewed as the convolution of a low-pass PSF with the actual image, where both the PSF and the actual image are unknown in practice. The PSF of a SPECT system is determined by the combined effect of several factors, which include the gamma camera PSF, the scattering, and pinhole PSF for pinhole SPECT systems, and therefore is hard to be determined analytically. Inspired by the blind deconvolution algorithm, we formulate a blind deblurring reconstruction algorithm, which also consists of two iterative update sequences, which are corresponded for the PSF and the SPECT reconstruction, respectively. In the phantom study, the algorithm reduces image blurring and preserves the edges without introducing extra artifacts. The localized measurement shows that the performance of reconstruction image improved by up to 50%. In experimental studies, the contrast and quality of reconstruction is substantially improved. Therefore, algorithm shows promising in tumor localization and quantification.