In this study, we will employ the threshold cointegraion and threshold error correction model to examine the co-movement and the long-run relationship among eight major industrial group stock indexes in Taiwan stock market. In previous studies, vector autoregression model and Granger Causality are the most used models and tests for evaluating the long-run equilibrium tendency among those major industrial groups. They found there exists the weak form market efficiency in Taiwan stock market. However, in real world the relationship cannot be appropriately expressed by the single-status linear models. In this study, we add the concept of threshold to the empirical model. It appears from the evidence the that the short-term co-movement will not be changed for the model with thresholds, but long-term equilibrium tendency may become obvious during some ranges.