Purpose: To develop a fast, deep-learning approach for quantitative magnetization-transfer contrast (MTC)-MR fingerprinting (MRF) that simultaneously estimates multiple tissue parameters and corrects the effects of B-0 and B-1 variations.Methods: An only-train-once recurrent neural network was designed to perform the fast tissue-parameter quantification for a large range of different MRF acquisition schedules. It enabled a dynamic scan-wise linear calibration of the scan parameters using the measured B-0 and B-1 maps, which allowed accurate, multiple-tissue parameter mapping. MRF images were acquired from 8 healthy volunteers at 3 T. Estimated parameter maps from the MRF images were used to synthesize the MTC reference signal (Z(ref)) through Bloch equations at multiple saturation power levels.Results: The B-0 and B-1 errors in MR fingerprints, if not corrected, would impair the tissue quantification and subsequently corrupt the synthesized MTC reference images. Bloch equation-based numerical phantom studies and synthetic MRI analysis demonstrated that the proposed approach could correctly estimate water and semisolid macromolecule parameters, even with severe B-0 and B-1 inhomogeneities.Conclusion: The only-train-once deep-learning framework can improve the reconstruction accuracy of brain-tissue parameter maps and be further combined with any conventional MRF or CEST-MRF method.