This work proposes a maximum a posteriori (MAP) based parameter learning algorithm for acoustic-to-articulatory inversion. Inversion method is based on single global linear dynamic system (GLDS) representation of acoustic and articulatory data. MAP based learning algorithm considers a prior distribution for the parameter set as well as the likelihood of the training data. Therefore in this paper, we investigate the selection of prior distributions with hyperparameters for GLDS to improve the performance of articulatory inversion. The performance of the proposed learning algorithm and comparison of it with the maximum likelihood (ML) based learning method are examined on an extensive set of examples. These results show that the performance of the articulatory inversion method based on GLDS is significantly improved via MAP based learning algorithm.