As quantum computing progresses, the assessment of cryptographic algorithm resilience against quantum attack gains significance interests in the field of cryptanalysis. Consequently, this paper proposes the depth-optimized quantum circuit of Korean hash function (i.e., LSH) and estimates its quantum attack cost in quantum circuits. By utilizing an optimized quantum adder and employing parallelization techniques, the proposed quantum circuit achieves a 78.8% improvement in full depth and a 79.1% improvement in Toffoli depth compared to previous the-state-of art works. In conclusion, based on the proposed quantum circuit, we estimate the resources required for a Grover collision attack and evaluate the post-quantum security of LSH algorithms.