#SMT problem is an extension of SMT problem. It needs to compute the number of satisfiable solutions for a given first-order logic formula. Now the problem has been widely applied in the compiler optimization, hardware design, software verification, and automated reasoning. With widespread application of #SMT problem, the design of #SMT solver for large-scale instances is needed. This work presents a design of an approximate solver (VolComputeWithLocalSearch) for solving large-scale #SMT instances. It adds the differential evolution algorithm into the existing exact solution algorithm for #SMT, and gives the approximate solution by calling the volume calculation tool qhull. The algorithm reduces the number of volume calculations by bunch rule and enumerates all regions with solutions by differential evolution algorithm. This paper also proves in theory that the solution of new algorithm is the lower bound of the exact solution, thus it can be used in software testing and other fields which only need to know the lower bound. The experimental results show that VolComputeWithLocalSearch solver is stable, fast, and has a good performance in high dimension problems.