Covering arrays (CAs) are often used as test suites for combinatorial interaction testing to discover interaction faults of real-world systems. Most real-world systems involve constraints, so improving algorithms for covering array generation (CAG) with constraints is beneficial. Two popular methods for constrained CAG are greedy construction and meta-heuristic search. Recently, a meta-heuristic framework called two-mode local search has shown great success in solving classic NPhard problems. We are interested whether this method is also powerful in solving the constrained CAG problem. This work proposes a two-mode meta-heuristic framework for constrained CAG efficiently and presents a new meta-heuristic algorithm called TCA. Experiments show that TCA significantly outperforms state-of-the-art solvers on 3-way constrained CAG. Further experiments demonstrate that TCA also performs much better than its competitors on 2-way constrained CAG.