  Assume $(M, \omega)$ is a connected, compact 6 dimensional symplectic
manifold equipped with a semi-free Hamiltonian circle action, such that the
fixed point set consists of isolated points or compact orientable surfaces. We
restrict attention to the case $\dim$ $H^2(M)<3$. We give a complete list of
the possible manifolds, determine their equivariant cohomology ring and
equivariant Chern classes. Some of these manifolds are classified up to
diffeomorphism. We also show the existence for a few cases.
