Conjugate heat transfer (CHT) is the simultaneous, coupled heat transfer within a fluid and an adjoining solid, and the interface treatment plays an important role in its analysis, particularly when using unstructured grid system. In the present paper a new solid-fluid interface treatment in CHT analysis is presented and applied to two typical CHT problems, i.e. natural convections in both concentric thick-walled cylinders and cavity with a centered solid body. The present interface treatment for unstructured mesh clearly demonstrates the same accuracy and robustness as that for typical structured mesh.