Parameter estimation in Generalized Autoregressive Conditional Heteroscedastic (GARCH) model has received much attention in the literature. Commonly used quasi maximum likelihood estimator (QMLE) may not be suitable if the model is misspecified. Alternatively, we can consider using variance targeting estimator (VTE) as it seems to be a better fit for misspecified initial parameters. This paper extends the application to see how both QMLE and VTE perform under error distribution misspecifications. Data are simulated under two error distribution conditions: one is to have a true normal error distribution and the other is to have a true student-t error distribution with degree of freedom equals to 3. The error distribution assumption that has been selected for this study are: normal distribution, student-t distribution, skewed normal distribution and skewed student-t. In addition, this study also includes the effect of initial parameter specification. The analyses are divided into two case designs. Case 1 is when w_0=0.1,a_0=0.05,ß_0=0.85 to represent the well specified initial parameters while Case 2 is when w_0=1,a_0=0,ß_0=0 to represent misspecified initial parameters. The results show that both QMLE and VTE estimator performances for misspecified initial parameters may not improve in well specified error distribution assumptions. Nevertheless, VTE shows a favourable performance compared to QMLE when the error distribution assumption is not the same as true underlying error distribution.