  We study the concurrence of arbitrary-dimensional multipartite quantum
states. Analytical lower bounds of concurrence for tripartite quantum states
are derived by projecting high-dimensional states to $2\otimes 2\otimes 2$
substates. The results are then generalized to arbitrary multipartite quantum
systems. Furthermore, the scheme enables us obtain lower bounds of concurrence
for arbitrary four-partite quantum states by projecting high-dimensional states
to arbitrary given lower dimensional substates. By detailed examples we show
that our results improve the existing lower bounds of concurrence.
