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In magnetic particle imaging (MPI), image blurring and artifacts occur in a reconstructed image because the magnetization signals generated from magnetic nanoparticles (MNPs) at the field free point (FFP) are similar to those around the FFP regions. In order to overcome these problems, we proposed a new reconstruction method using neural networks. In this method, a data set of magnetization signals and MNP location pairs is used for learning in neural networks. If all possible combinations of the data sets are learned, an accurate estimated result is obtained. However, it is difficult to learn all the combinations in a reasonable period of time. In this study, the number of data sets learned in the first stage was minimized, and additional learning using the appropriate data sets, which reduces the error between observed signals and estimated signals, was performed. By learning the minimum number of required data sets, it is expected that image blurring and artifacts will be suppressed even when the MNP’s magnetization is insufficient, e.g., when an applied alternative magnetic field and/or a gradient magnetic field are/is weak. We performed numerical experiments to confirm the effectiveness of our proposed method. From the experimental results, it was confirmed that image blurring and artifacts were suppressed using our proposed method even when the MNP’s magnetization was insufficient. However, it may be difficult to reconstruct an accurate image when appropriate data sets are not selected for learning. Hence, in the future, we will improve the method for selecting the data sets.