Abstract Starting from the dispersion relation we have discussed low energies π-N scattering amplitude with isospin positive part. It is shown that for P1/2+ -wave, the results evaluating from CGLN formula are essentially in agreement with experiments. But for S-wave, when comparing with experiments, even the sign of CGLN results is wrong. Further they are increasing as energy very rapidly that exceeds the limit allowed by the unitary condition. From analysis it is shown that one cannot solve this problem and at the same time keep the agreeing of the calculated P1/2+-wave results with the experiments by introducting a π-π S-wave interaction. But alternatively if we attacked from the π-N S-partial wave dispersion relation with one subtraction, then the results agree with the experiments fairly well. So it is likely that the π-π S-wave interaction plays an unimportant role in it.