Predicting the prices of cryptocurrency owing to its volatility, instability, and other factors has been challenging; investors and traders especially in Nigeria have been on a constant look for a more reliable way of knowing market trends and prices and while there has been so many research conducted using deep learning, the results for which has fall short of what investors could called a strong predictor. This research reviewed the results of many works that had been done and proposed two types of recurrent neural network (RNNs) namely Long Short-Term Memory and Gated Recurrent Unit (GRU) for predicting the future prices of two of the most common crypto assets namely Bitcoin (BTC) and Ethereum (ETH), these two were selected based on their popularity, the volume traded and their market capitalization. The experiment was conducted in a GPU Jupyter Notebook environment and the performance of our experiment was evaluated on a test set using root mean square error (RMSE) and based on its values, the LSTM presented a better performance with rsme scores of 654.66, and 80.30 respectively for BTC and ETH as compared to GRU. The paper proceeds further to compare the results of this experiment with other related works and we discovered that its performance is a great improvement.