A goodness-of-fit test, based on sample entropy, for normality was given by Vasicek. The test, however, can be applied only to the composite hypotesis. In this paper a new test of fit for normality is introduced based on Kullback-Leibler inforamtion. The Kullback-Leibler information is an extended concept of entropy, and so the test can be applied not only to the composite hypotesis but also to the simple hypothesis. The power comparisons of the proposed test with the some other tests are illustrated and discussed.