During the operation of a system including a deep neural network (DNN), new input values that were not included in the training dataset are given to the DNN. In such a case, the DNN may be incrementally trained with the new input values; however, that training may reduce the accuracy of the DNN in regard to the dataset that was previously obtained and used for the past training. It is necessary to evaluate the effect of the additional training on the accuracy for the past dataset. However, evaluation by testing all the input values included in the past dataset takes time. Therefore, we propose a new method to quickly evaluate the effect on the accuracy for the past dataset. In the proposed method, the gradient of the parameter values (such as weight and bias) for the past dataset is extracted by running the DNN before the training. Then, after the training, its effect on the accuracy with respect to the past dataset is calculated from the gradient and update differences of the parameter values. To show the usefulness of the proposed method, we present experimental results with several datasets. The results show that the proposed method can estimate the accuracy change by additional training in a constant time.