  We find a class of non-relativistic supersymmetric solutions of IIB
supergravity with non-trivial B-field that have dynamical exponent n=2 and are
invariant under the Schrodinger group. For a general Sasaki-Einstein internal
manifold with U(1)^3 isometry, the solutions have two real supercharges. When
the internal manifold is S^5, the number of supercharges can be four. We also
find a large class of non-relativistic scale invariant type IIB solutions with
dynamical exponents different from two. The explicit solutions and the values
of the dynamical exponents are determined by vector eigenfunctions and
eigenvalues of the Laplacian on an Einstein manifold.
