Specification and forecast ionospheric parameters, such as ionospheric electron density (Ne), have been an important topic in space weather and ionosphere research. Neural networks (NNs) emerge as a powerful modeling tool for Ne prediction. However, heavy manual attention costs time to determine the optimal NN structures. In this work, we propose to use neural architecture search (NAS), an automatic machine learning method, to address this problem of NN models. NAS aims to find the optimal network structure through the alternated optimization of the hyperparameters and the corresponding network parameters. A total of 16-year data from Millstone Hill incoherent scatter radar (ISR) are used for NN models. One single-layer NN (SLNN) model and one deep NN (DNN) model are trained with NAS, namely SLNN-NAS and DNN-NAS, for Ne prediction and compared with their counterparts without NAS from previous studies, denoted as SLNN and DNN. Our results show that SLNN-NAS and DNN-NAS outperformed SLNN and DNN, respectively. NN models can reveal more finer details than the empirical ionospheric model developed using traditional data fitting approaches. DNN-NAS yields the best prediction accuracy measured by quantitative metrics and rankings of daily pattern prediction. The limited improvement of NAS is likely due to the network complexity and the limitation of fully connected NN without a memory mechanism.