MR parameter mapping (e.g., T1 mapping, T2 mapping, or T*2 mapping) is a valuable tool for tissue characterization. However, its practical utility has been limited due to long data acquisition time. This paper addresses this problem with a new model-based parameter mapping method, which utilizes an explicit signal model and imposes a sparsity constraint on the parameter values. The proposed method enables direct estimation of the parameters of interest from highly undersampled, noisy k-space data. An algorithm is presented to solve the underlying parameter estimation problem. Its performance is analyzed using estimation-theoretic bounds. Some representative results from T2 brain mapping are also presented to illustrate the performance of the proposed method for accelerating parameter mapping.