Compressed sensing (CS) holds considerable promise to accelerate the data acquisition in magnetic resonance imaging by exploiting signal sparsity. Prior knowledge about the signal can be exploited in some applications to choose an appropriate sparsifying transform. This work presents a CS reconstruction for magnetic resonance (MR) parameter mapping, which applies an overcomplete dictionary, learned from the data model to sparsify the signal. The approach is presented and evaluated in simulations and in in vivo T(1) and T(2) mapping experiments in the brain. Accurate T(1) and T(2) maps are obtained from highly reduced data. This model-based reconstruction could also be applied to other MR parameter mapping applications like diffusion and perfusion imaging.