A unital separable (C^ast)-algebra, (A) is said to be locally AH with no dimension growth if there is an integer (d>0) satisfying the following: for any (epsilon >0) and any compact subset ({mathcal F}subset A,) there is a unital (C^ast)-subalgebra, (B) of (A) with the form (PC(X, M_n)P), where (X) is a compact metric space with covering dimension no more than (d) and (Pin C(X, M_n)) is a projection, such that (mathrm{dist}(a, B)