We present a method for calculating scattering phase shifts which utilizes continuum-discretized states obtained in a bound-state type calculation. The wrong asymptotic behavior of the discretized state is remedied by means of the Green's function formalism. Test examples confirm the accuracy of the method. The α+n scattering is described using realistic nucleon–nucleon potentials. The 3/2− and 1/2− phase shifts obtained in a single-channel calculation are too small in comparison with experiment. The 1/2+ phase shifts are in reasonable agreement with experiment, and gain contributions both from the tensor and central components of the nucleon–nucleon potential.