  We study the nonlocality of arbitrary dimensional bipartite quantum states.
By computing the maximal violation of a set of multi-setting Bell inequalities,
an analytical and computable lower bound has been derived for general two-qubit
states. This bound gives the necessary condition that a two-qubit state admits
no local hidden variable models. The lower bound is shown to be better than
that from the CHSH inequality in judging the nonlocality of some quantum
states. The results are generalized to the case of high dimensional quantum
states, and a sufficient condition for detecting the non-locality has been
presented.
