This paper use GJR-GARCH in mean model to examines the causal relationship between financial development and economic growth in Taiwan for the period 1978Q1 – 2007Q3. It focuses on the effects of two aspects of financial development on growth: stock market and banking sector. GJR-GARCH in mean model has advantages over traditional measures. By including the conditional variance. In the mean equation, and was shown to retrieve more efficient estimator than traditional OLS. Also, the GJR-GARCH in mean framework emphasizes the asymmetry of the volatility response to news, which allows positive and negative unanticipated returns to have different impacts on the conditional variance. The result demonstrates that the GJR-GARCH is more appropriate than the other GARCH models and confirms the presence of conditional variance in the mean equation. The cointegration test provides evidence of the non-existence of a long-run equilibrium relationship between financial development and economic growth. The empirical results suggest that leverage effect was present and shocks have asymmetric impact on the volatility.