KLEIN has experienced attacks such as truncated difference cryptanalysis and integral cryptanalysis since it was proposed. Its encryption structure has actual security, but the vulnerability of the key expansion algorithm leads to full-round key recovery attacks. Firstly, the key expansion algorithm was modified and an improved algorithm N-KLEIN was proposed. Secondly, an efficient quantum circuit was implemented on the S-box using the in-place method, which reduced the width and depth of the circuit and improved the implementation efficiency of the quantum circuit. Thirdly, the quantization of obfuscation operations was achieved using LUP decomposition technology. Then, an efficient quantum circuit was designed for N-KLEIN, and an efficient quantum circuit for all round N-KLEIN was proposed. Finally, the resource occupation for the quantum implementation of full-round N-KLEIN was evaluated and compared with the resources occupied by existing quantum implementations of lightweight block ciphers such as PRESENT and HIGHT. At the same time, an in-depth study was conducted on the cost of key search attacks based on Grover algorithm, and the cost of N-KLEIN-{64,80,96} using Grover algorithm to search for keys under the Clifford+T model was given, and then the quantum security of N-KLEIN was evaluated. Comparative results indicate that the quantum implementation cost of N-KLEIN algorithm is significantly lower.