In this study open-source software (QSPECT) suitable for the iterative reconstruction of single-photon emission computed tomography (SPECT) data is presented. QSPECT implements maximum likelihood expectation maximization and ordered subsets expectation maximization algorithms in a user-friendly graphical interface. The software functionality is described and validation results are presented. Maximum likelihood expectation maximization and ordered subsets expectation maximization algorithms are implemented in C++. The Qt toolkit, a standard C++ framework for developing high-performance cross-platform applications, has been used for the graphical user interface development. QSPECT is tested using original projection data from two clinical SPECT systems: (i) APEX SPX-6/6HR and (ii) Millennium MG. Phantom experiments were carried out to evaluate the quality of reconstructed images in terms of (i) spatial resolution, (ii) sensitivity to activity variations, and (iii) the presence of scatter media. A cardiac phantom was used to simulate a normal and abnormal scenario. Finally, clinical cardiac SPECT images were reconstructed. In all cases, QSPECT results were compared with the clinical systems reconstruction software that uses the standard filtered backprojection algorithm. The reconstructed images show that QSPECT, when compared with standard clinical reconstruction, provides images with higher contrast, reduced background, and better separation of small sources located in small distances. In addition, reconstruction with QSPECT provides more quantitative images, and reduces the background created by scatter media. Finally, the phantom and clinical cardiac images are reconstructed with similar quality. QSPECT is a freely distributed, open-source standalone application that provides real-time, high-quality SPECT images. The software can be further modified to improve reconstruction algorithms, and include more correction techniques, such as, scatter and attenuation correction.