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.