Financial time series are often found to be heavy-tailed and skewed. Motivated from Skewed-t and Asymmetric Laplace distributions, two new M-estimators, called ST and AL, respectively, are introduced for estimation of GARCH-type models. Performance of estimators is checked with commonly used quasi-maximum likelihood, least absolute deviation and other robust estimators, for both symmetric and asymmetric models through a Monte Carlo study. Results of simulation revealed that both estimators provide accurate parameter estimates of GARCH models outperforming competing estimators when errors are generated from non-normal distributions. An application to real data set shows that these estimators also give better Value-at-Risk forecasts.