  This paper introduces the concept of average conformal hyperbolic sets, which
admit only one positive and one negative Lyapunov exponents for any ergodic
measure. For an average conformal hyperbolic set of a C1 diffeomorphism,
utilizing the techniques in sub-additive thermodynamics formalism and some
geometric arguments with unstable/stable manifolds, a formula of the Hausdorff
dimension and lower (upper) box dimension is given in this paper, which are
exactly the sum of the dimensions of the restriction of the hyperbolic set to a
stable and unstable manifolds. Furthermore, the dimensions of an average
conformal hyperbolic set varies continuously with respect to the dynamics.
