Purpose To develop a set of artificial neural networks, collectively termed qMTNet, to accelerate data acquisition and fitting for quantitative magnetization transfer (qMT) imaging. Methods Conventional and interslice qMT data were acquired with two flip angles at six offset frequencies from seven subjects for developing the networks and from four young and four older subjects for testing the generalizability. Two subnetworks, qMTNet-acq and qMTNet-fit, were developed and trained to accelerate data acquisition and fitting, respectively. qMTNet-2 is the sequential application of qMTNet-acq and qMTNet-fit to produce qMT parameters (exchange rate, pool fraction) from undersampled qMT data (two offset frequencies rather than six). qMTNet-1 is one single integrated network having the same functionality as qMTNet-2. qMTNet-fit was compared with a Gaussian kernel-based fitting. qMT parameters generated by the networks were compared with those from ground truth fitted with a dictionary-driven approach. Results The proposed networks achieved high peak signal-to-noise ratio (>30) and structural similarity index (>97) in reference to the ground truth. qMTNet-fit produced qMT parameters in concordance with the ground truth with better performance than the Gaussian kernel-based fitting. qMTNet-2 and qMTNet-1 could accelerate data acquisition at threefold and accelerate fitting at 5800- and 4218-fold, respectively. qMTNet-1 showed slightly better performance than qMTNet-2, whereas qMTNet-2 was more flexible for applications. Conclusion The proposed single (qMTNet-1) and two joint neural networks (qMTNet-2) can accelerate qMT workflow for both data acquisition and fitting significantly. qMTNet has the potential to accelerate qMT imaging for clinical applications, which warrants further investigation.