Optimization of a prediction (forecasting) is very important to do so that the predicted results obtained to be better and quality. In this study, the authors optimize previous research that has been done by the author using backpropagation algorithm. The optimization process will use Conjugate Gradient Beale-Powell Restarts. Data to be predicted is Consumer Price Index data based on health group from Medan Central Bureau of Statistics from 2014 until 2016. Previous research using 8 architectural models, namely: 12-5-1, 12-26-1, 12-29 -1, 12-35-1, 12-40-1, 12-60-1, 12-70-1 and 12-75-1 with best architectural models 12-70-1 with an accuracy of 92%. In contrast to previous research concentrating on finding accuracy using backpropagation, this study will optimize the backpropagation with Conjugate Gradient Beale-Powell Restart, which not only focuses on accuracy but also the convergence of the two algorithms and the translation of predicted results, which is not done in a previous study. This research will use the same architectural model as the previous research and will get the result with the accuracy of 92% with the best architectural model that is 12-70-1 (same as previous research). Thus, this model is good enough for prediction even with different algorithms, since the accuracy of converging backpropagation with Conjugate Gradient Beale-Powell Restarts.