Recently, Liu and Yin (Int. J. Theor. Phys. 60, 2074-2083 (2021)) proposed a two-party private set intersection protocol based on quantum Fourier transform. We find the participant can deduce the other party's private information, which violates the security requirement of private set computation. In order to solve this problem, an improved private set intersection protocol based on Hadamard gate is proposed. Firstly, the more feasible Hadamard gates are used to perform on the original n qubits instead of the quantum Fourier transform, which may reduce the difficulty of implementation. In addition, through the exclusive OR calculation, the participant's private information is randomly chosen and encoded on the additional n qubits, which prevents participants from obtaining the result of the difference set S-diff , and then avoids the internal leakage of private information. Finally, the correctness and security analysis are conducted to show the proposed protocol can guarantee the correctness of computation result as well as resist outside attacks and participant internal attacks.