We propose a new way of description of the global entanglement property of a multi-partite pure state quantum system. Based on the idea of bipartite concurrence, by dividing the multi-partite quantum system into two subsystems, a combination of all the bipartite concurrences of a multi-partite quantum system is used to describe the entanglement property of the multi-partite system. We derive the analytical results for GHZ-state, W-state with arbitrary number of qubits, and cluster state with the number of particles no greater than 6.