  We present a lattice QCD calculation of the scattering phase shift for the
I=2 $S$-wave two-pion system using the finite size method proposed by
L\"uscher. We work in the quenched approximation employing the standard
plaquette action at $\beta=5.9$ for gluons and the Wilson fermion action for
quarks. The phase shift is extracted from the energy eigenvalues of the
two-pion system, which are obtained by a diagonalization of the pion 4-point
function evaluated for a set of relative spatial momenta. In order to change
momentum of the two-pion system, calculations are carried out on $24^3\times
60$, $32^3\times 60$, and $48^3\times 60$ lattices. The phase shift is
successfully calculated over the momentum range $0 < p^2 < 0.3 {\rm GeV}^2$.
