In the R-language, many packages exist for the estimation and forecasting of GARCH processes, including fGarch and rugarch. However, none, to our knowledge, have addressed the issue of robustness toward additive outliers, rather than innovations outliers. Muler and Yohai (2008) proposed two approaches to robust GARCH(p,q) model fitting to avoid bias in the parameter estimates and the preceding kind of over-estimation of volatility following isolated large outlier returns. In the first approach, parameters are obtained by maximum likelihood function using a modified likelihood function based on a bounded loss function. The second approach improves on the first by using a filter that limits the effect of an additive outlier on subsequent predictors of conditional variance. Our proposal is to implement the two approaches by exposing interfaces to a C++ library that can be called from any higher level language for estimating the likelihood functon. We will first develop an R implementation of the robust GARCH(p, q) fitting method, with application examples, and evaluate the performance of the code using as bench- marks selected simulation results from Muler and Yohai.