Over the past few years, with the advent of blockchain technology, there has been a massive increase in the usage of Cryptocurrencies. However, Cryptocurrencies are not seen as an investment opportunity due to the market's erratic behavior and high price volatility. Most of the solutions reported in the literature for price forecasting of Cryptocurrencies may not be applicable for real-time price prediction due to their deterministic nature. Motivated by the aforementioned issues, we propose a stochastic neural network model for Cryptocurrency price prediction. The proposed approach is based on the random walk theory, which is widely used in financial markets for modeling stock prices. The proposed model induces layer-wise randomness into the observed feature activations of neural networks to simulate market volatility. Moreover, a technique to learn the pattern of the reaction of the market is also included in the prediction model. We trained the Multi-Layer Perceptron (MLP) and Long Short-Term Memory (LSTM) models for Bitcoin, Ethereum, and Litecoin. The results show that the proposed model is superior in comparison to the deterministic models.