  We study a class of dilatation invariant BPS surface operators in
4-dimensional N=4 Super Yang-Mills theory and their holographic duals in type
IIB string theory in AdS_5 x S^5. First we take an example of 1/4 BPS surface
operator and study it in detail from the holographic point of view. The gravity
dual of this surface operator is a D3-brane characterized by a holomorphic
submanifold. The supersymmetry and vacuum expectation value are checked in both
the gauge theory side and the gravity side. We also calculate the correlation
functions with the chiral primary operators in both sides and find good
agreement. Next we consider more general dilatation invariant BPS surface
operators. The gravity duals of those operators are proposed.
