  We propose to study hadron-hadron scattering using lattice QCD in an
asymmetric box which allows one to access more non-degenerate low-momentum
modes for a given volume. The conventional L\"{u}scher's formula applicable in
a symmetric box is modified accordingly. To illustrate the feasibility of this
approach, pion-pion elastic scattering phase shifts in the I=2, J=0 channel are
calculated within quenched approximation using improved gauge and Wilson
fermion actions on anisotropic lattices in an asymmetric box. After the chiral
and continuum extrapolation, we find that our quenched results for the
scattering phase shifts in this channel are consistent with the experimental
data when the three-momentum of the pion is below 300MeV. Agreement is also
found when compared with previous theoretical results from lattice and other
means. Moreover, with the usage of asymmetric volume, we are able to compute
the scattering phases in the low-momentum range (pion three momentum less than
about 350MeV in the center of mass frame) for over a dozen values of the pion
three-momenta, much more than using the conventional symmetric box with
comparable volume.
