The Quantum Approximate Optimization Algorithm is the hybrid classic-quantum algorithm that is used for solving the combinatorial optimization problem. However, the algorithm performs poorly in the constrained combinatorial optimization problem because it considers all solutions with the same initial probability. In this article, we propose a new quantum state that improves the QAOA performance and does not require slack variables for inequality constraints. We also introduce some properties of our new quantum state in solving a constrained combinatorial optimization problem. To see our method’s efficiency, we use our method to solve the quadratic knapsack problem and compare it with the quantum state method of Hao et al. [5] which is one of the most recent and effective methods for solving the constrained combinatorial optimization.