In contrast to Gaussian or Woods-Saxon potential a two-term four parameter nuclear Hulthén type interaction is considered to describe the α-α, α-3 He and α-3 H systems. By exploiting the phase function method, scattering phase shifts are computed up to E Lab = 100 MeV for the α-α system and E Lab = 15 MeV for α-3 He and α-3 H systems. The S-wave phase shift δ0 for the α-α system tends to 2π and δ 3/2 − for the α-3 He system tends to π, in the limit of zero energy. Reasonable agreements in phase shifts with the standard data are obtained with this simple potential model except for the 5/2 − states of α-3 He and α-3 H systems. With an additional energy-dependent correction factor to our potential, a good agreement with experimental data is obtained for 5/2 − states. We have also compared our results with the convenient Born approximations.