Abstract: In this paper, it is assumed that the left-cut of π-N scattering can be better approximated by four effective poles than by only one or two poles in the usual way. The author has made calculation for the contribution due to the short range interactions of the cross-diagram. The resulting phase-shift agrees with the experiment[3], and indicates that low-energy p-wave 3-3 resonance exists. Furthermore, from the calculated results, it can be seen that, to make better approximation, at least four poles must be taken, therefore the behaviour of the amplitude of the left-cut is very complicated.