One of the recent financial technologies is Block chain-based currency known as Cryptocurrency that these days because of their unique features has become quite popular. The first known Cryptocurrency in the world is Bitcoin, and since the cryptocurrencies market is a contemporary one, Bitcoin is currently considered as the pioneer of this market. Since the value of the previous Bitcoin prices data have a non-linear behaviour, this study aims at predicting Bitcoin price using Grey model, Back Propagation Artificial Neural Network and Integrated Model of Grey Neural Network. Then, the prediction’s accuracy of these methods will be measured using MAPE and RMSE indices and also Bitcoin price data for a five-year period (2014-2018). The results had indicated that wen estimating Bitcoin daily prices, Back Propagation Artificial Neural Network model has the lowest absolute error rate (5.6%) compared to the Grey model and the integrated model. Additionally, for the monthly prediction of Bitcoin price, the integrated model, with the lowest absolute error rate (9%), has a better performance than the two other models.