The Cryptocurrency Volatility Index (CVI index) has been introduced to estimate the 30-day future volatility of the cryptocurrency market. In this article, we introduce a new Deep Neural Network with an attention mechanism to forecast future values of this index. We then look at the stability and performance of our proposed model against the benchmark models widely used for time series prediction. The results show that our proposed model performs well when compared to popular methods such as traditional Long Short Term Memory, Temporal Convolution Network, and other statistical methods like Simple Moving Average, Random Forest and Support Vector Regression. Furthermore, we show that the well-known Simple Moving Average method, while it has its own advantages, has the weak spot when dealing with time series with large fluctuations.