For a contact manifold, we have two fundamental structures associated with the given contact form. One is a Riemannian structure and the other is a CR structure. In this talk, we study CR geometry, which preserves a transversal almost complex structure. Using the Tanaka-Webster connection as a canonical connection, we study it's curvature tensor, the Ricci tensors, and the Chern-Moser-Tanaka invariant. Then we examine their geometric properties.