Magneto-acousto-electrical computed tomography (MAE-CT) is a recently developed rotational magneto-acousto-electrical tomography (MAET) method, which can map the conductivity parameter of tissues with high spatial resolution. Since the imaging mode of MAE-CT is similar to that of CT, the reconstruction algorithms for CT are possible to be adopted for MAE-CT. Previous studies have demonstrated that the filtered back-projection (FBP) algorithm, which is one of the most common CT reconstruction algorithms, can be used for MAE-CT reconstruction. However, FBP has some inherent shortcomings of being sensitive to noise and non-uniform distribution of views. In this study, we introduced iterative reconstruction (IR) method in MAE-CT reconstruction and compared its performance with that of the FBP. The numerical simulation, the phantom, and in vitro experiments were performed, and several IR algorithms (ART, SART, SIRT) were used for reconstruction. The results show that the images reconstructed by the FBP and IR are similar when the data is noise-free in the simulation. As the noise level increases, the images reconstructed by SART and SIRT are more robust to the noise than FBP. In the phantom experiment, noise and some stripe artifacts caused by the FBP are removed by SART and SIRT algorithms. In conclusion, the IR method used in CT is applicable in MAE-CT, and it performs better than FBP, which indicates that the state-of-the-art achievements in the CT algorithm can also be adopted for the MAE-CT reconstruction in the future.