Quantitative magnetization transfer (qMT) imaging overcomes the drawbacks of traditional MT imaging by producing more quantitative parameters. However, data acquisition and processing can be time-consuming, which limits its usage. In this study, an artificial neural network, qMTNet, is proposed to accelerate both the acquisition and fitting of qMT data. For data acquired from both conventional and inter-slice acquisition strategies, our approach demonstrated consistent fitting results with those from a previous dictionary-driven fitting method. The network reduces the time for both data acquisition and qMT fitting by a factor of 3 and 5000 times, respectively, compared to the conventional methods.