Since non-permutative quantum gates have more complex rules than permutative quantum gates, direct use of non-permutative quantum gates can greatly increase the complexity of the synthesis algorithm, so given quantum gates should be used to create new permutative quantum gates, and then these permutative gates are used to synthesize the desired quantum reversible logic circuit, thus improving the algorithm performance. This paper focuse on how to use non-permutative quantum gates to construct new permutative gates, therefore, we absorb the idea of Gray code and present an efficient recursive construction which can use controlled-NOT gates and controlled K-th-root-of-NOT gates (non-permutative quantum gates) to construct the optimal Toffoli-like gates (permutative quantum gates).