In the study, we proposed a regularization method for MAP-MRI estimation, called ReMAP. This method includes a regularization term in the cost functional in order to penalize the coefficients. The penalty is a simple diagonal matrix with entries determined only by the order of the Hermite functions, where higher order functions take more penalization, therefore, this method is easy to implement. In addition, ReMAP outperforms MAP-MRI in both estimation efficiency and accuracy, revealing that the regularization term is crucial for a robust estimation. Therefore, ReMAP is an improved version of MAP-MRI and would be beneficial for clinical studies.