The empirical mode decomposition is applied to analyze the intrinsic multi-scale dynamic behaviors of complex financial systems. In this approach, the time series of the price returns of each stock is decomposed into a small number of intrinsic mode functions, which represent the price motion from high frequency to low frequency. These intrinsic mode functions are then grouped into three modes, i.e., the fast mode, medium mode and slow mode. The probability distribution of returns and auto-correlation of volatilities for the fast and medium modes exhibit similar behaviors as those of the full time series, i.e., these characteristics are rather robust in multi time scale. However, the cross-correlation between individual stocks and the return-volatility correlation are time scale dependent. The structure of business sectors is mainly governed by the fast mode when returns are sampled at a couple of days, while by the medium mode when returns are sampled at dozens of days. More importantly, the leverage and anti-leverage effects are dominated by the medium mode.