In this paper, a generalized GARCH-based stochastic mortality model is developed, which incorporates conditional heteroskedasticity and conditional non-normality. First, a detailed empirical analysis of the UK mortality rates from 1922 to 2009 is provided, where it was found that both the conditional heteroskedasticity and conditional non-normality are important empirical long-term structures of mortality. To describe conditional non-normality, a double-exponential distribution that allows conditional skewness and the heavy-tailed features found in the datasets was selected. For the practical implementation of the proposed model, a two-stage scheme was introduced to estimate the unknown parameters. First, the Quasi-Maximum Likelihood Estimation (QMLE) method was employed to estimate the GARCH structure. Next, the MLE was adopted to estimate the unknown parameters of the double-exponential distribution using residuals as input data. The model was then back-tested against the previous 10 years of mortality data to assess its forecasting ability, before Monte Carlo simulation was carried out to simulate and produce a table of forecast mortality rates from the optimal distribution.