The purpose of this work was to develop and evaluate a novel deep learning-based reconstruction framework called Model-Augmented Neural neTwork with Incoherent k-space Sampling (MANTIS) for accelerated MR parameter mapping. Our approach combines end-to-end CNN mapping with k-space consistency using the concept of cyclic loss to further enforce data and model fidelity. Incoherent k-space sampling is used to improve reconstruction performance. A physical model is incorporated into the proposed framework, so that the parameter maps can be efficiently estimated directly from undersampled images. The performance of MANTIS was demonstrated for T2 mapping of the knee joint. Our study demonstrated that the proposed MANTIS framework represents a promising approach for efficient MR parameter mapping. MANTIS can potentially be extended to other types of parameter mapping with appropriate models.