Bitcoin has emerged as the foremost digital currency in the global financial sphere, with prognosticating its price becoming a pivotal focus in finance. This study delves into the pressing necessity for precise Bitcoin price forecasts, spurred by the notable volatility inherent in cryptocurrency markets. Such predictions play a crucial role in assisting investors to manage risks and make well-informed decisions. Moreover, accurate forecasts aid in the formulation of effective trading strategies and market analysis. Employing the Grey Wolf Optimizer (GWO), this research endeavors to forecast Ethereum’s day-ahead prices. By incorporating time-varying acceleration coefficients, the GWO algorithm seeks to strike a balance between exploration and exploitation, mimicking the reflex actions of wolves in nature. Additionally, to bolster the exploration process, a modified GWO (mGWO) algorithm integrates an exponential decay function to prevent premature convergence, thereby enhancing accuracy. Subsequently, this modified algorithm is employed to optimize Support Vector Regression (SVR) parameters, ensuring the model’s effectiveness in capturing intricate patterns within cryptocurrency data. Through the innovative mGWO-SVR approach, this study not only advances cryptocurrency price prediction techniques but also underscores the significance of algorithm refinement for optimal Bitcoin price forecasting outcomes. This methodology is poised to benefit intraday, interday, and short-term traders in stock markets.