We propose a Bayesian approach for improving the accuracy of diffusional kurtosis imaging in a small number of data acquisitions. Gaussian-approximated prior distributions are made from primary maximum-likelihood estimation (MLE). The approach was tested using a healthy volunteer data in which a part of signals was replaced with simulated glioma signals. Although the approach does not yield further improvement when MLE has a certain degree of accuracy, the approach has effect to reduce large misestimations and did not cause false shrinkage of dispersions that the sample parameters inherently have. The approach reduces the burden of data acquisition.