The object of the present paper is to study quarter symmetric nonmetric connection on a LP-Sasakian manifold. In this paper, we consider some properties of the curvature tensor, projective curvature tensor, concircular curvature tensor, conformai curvature tensor with respect to quarter symmetric non-metric connection in a LP-Sasakian manifolds. Finally we consider submanifolds with respect to quarter symmetric non-metric connection.