In 1970, semisymetric connection were studied by Yano [1] in a Riemannian manifold and in 1972 Mishra [2] studied affine connection in an almost contact Riemannian manifold. In the present paper we have defined a structure connnection in a Riemannian manifold and studied its properties in an almost contact metric manifold. It is seen that structure connection play fundamental role in an almost contact metric manifold.