Generalized autoregressive conditional heteroscedasticity in-mean model allows accounting for both time-varying variance and risk premium in financial time series data. This paper introduces an extension of this particular model with more flexible parameterization of the way variance enters the conditional mean equation, which allows for more complex dynamics in the time-varying risk premium. Paper presents model specification, criteria for hypothesis testing and develops an application for several stock exchange indexes. Results suggest evidence that proposed model may be more preferable to standard GARCH-in-mean model.