  In this paper, following the constructions of N. R. O'Brian, J. H. Rawnsley
and I. Vaisman, we define four almost Hermitian structures (up to conjugation)
on the twistor space of a Hermitian surface by using canonical connections,
including the Lichnerowicz connection and the Chern connection. We also study
the relations between the natural geometry of the twistor spaces and the
geometry of Hermitian surfaces.
