Existing time-domain simulation of LCC-HVDC systems faces a trade-off between accuracy and efficiency. The electromagnetic transient model can accurately emulate detailed dynamic processes, but its computational inefficiency makes it impractical for engineering applications. In contrast, the quasisteady-state model is computationally efficient but fails to adequately express the commutation process of LCC-HVDC systems and is incapable of performing in unbalanced fault scenarios. This paper proposes a neural network-based quasi-steady-state (NN-QSS) model to provide a powerful model for simulating, analyzing, and designing LCC-HVDC integrated power systems. Specifically, the NN-QSS model accurately captures and expresses the LCC-HVDC dynamic characteristics, especially in unbalanced fault scenarios, and is also capable of outputting the identification results of commutation failure occurrences as a sign during quasi-steady-state simulation. The proposed method has been validated using a modified IEEE 39-bus system, an actual provincial power system in China, and a CIGRE benchmark system based on hardware-in-the-loop. The experimental results show that the NN-QSS model is able to express dynamics close enough to electromagnetic transient models at the quasi-steadystate scale, and the commutation failure identification accuracy is improved by 18.8% relative to the existing methods.