Recently code transformations or tailored fitness functions are adopted to achieve coverage (structural or logical criterion) driven testing to ensure software reliability. However, some internal threats like negative impacts on underlying search strategies or local maximum exist. So we propose a dynamic symbolic execution (DSE) based framework combined with a path filtering algorithm and a new heuristic path search strategy, i.e., predictive path search, to achieve faster coverage-driven testing with lower testing cost. The empirical experiments (three open source projects and two industrial projects) show that our approach is effective and efficient. For the open source projects w.r.t branch coverage, our approach in average reduces 25.5% generated test cases and 36.3% solved constraints than the traditional DSE-based approach without path filtering. And the presented heuristic strategy, on the same testing budget, improves the branch coverage by 26.4% and 35.4% than some novel search strategies adopted in KLEE and CREST.