Combinatorial testing is a practical software testing approach that has been widely used in practice. Most research and applications of such approach focus on N-way combinatorial testing that provides a minimum coverage of all N-way interactions among factor. However, the strengths of different interactions may not be a fixed integer N, but a variable. Therefore, variable strength combinatorial testing approach is necessary in applications. Existing variable strength combinatorial testing, which allows some interactions have a higher strength than others, has a limitation that such higher-strength interactions must be disjoint. To avoid such a limitation, an improved variable strength combinatorial testing approach, which makes a more sufficient consideration on actual interaction relationship, is proposed in this article. Furthermore, two greedy heuristic algorithms are also proposed to generate combinatorial test suite. Compared to some existing algorithms and tools, the proposed algorithms have advantages on both the execution effectiveness and the optimality of generated test suite. Experimental results can prove such advantages.