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We combine the range-based GARCH model with the modified robust method of estimation and suggest a new approach to model volatility of returns. Thanks to this merger, we use more information which are commonly available alongside daily closing prices, i.e., low and high prices but at the same time we limit the influence of extreme observations on the estimation results. Owing to this, the procedure is not as sensitive to outliers as the maximum likelihood estimation of the range-based models. We also propose to introduce the change to the robust method, which adds elasticity in treating the outliers and serves to reflect the observations of financial markets, where, after occurrence of outliers, the volatility persists at an increased level. We apply this method to five selected cryptocurrencies: Bitcoin, Ethereum Classic, Ethereum, Litecoin and Ripple. The forecasts of variance based on the proposed approach are more accurate than forecasts from three benchmarks: the standard GARCH model, the standard range-based GARCH model and the GARCH model with the robust estimation.