  We shall introduce the notion of $C^\infty$ logarithmic symplectic structures
on a differentiable manifold which is an analog of the one of logarithmic
symplectic structures in the holomorphic category. We show that the generalized
complex structure induced by a $C^\infty$ logarithmic symplectic structure has
unobstructed deformations which are parametrized by an open set of the second
de Rham cohomology group of the complement of type changing loci if the type
changing loci are smooth. Complex surfaces with smooth effective anti-canonical
divisors admit unobstructed deformations of generalized complex structures such
as del pezzo surfaces and Hirzebruch surfaces. We also give some calculations
of Poisson cohomology groups on these surfaces.
  Generalized complex structures ${\cal J}_m$ on the connected sum $(2k-1)\Bbb
C P^2\# (10k-1)\ol {\Bbb C P^2}$ as in \cite{Cavalcanti_Gualtieri_2006},
\cite{Goto_Hayano} are induced by $C^\infty$ logarithmic symplectic structures
modulo the action of $b$-fields and it turns out that {generalized complex
structure}s ${\cal J}_m$ have unobstructed deformations of dimension
$12k+2m-3$.}
