Current combination therapy of PEG-INF and ribavirin against the Hepatitis C Virus (HCV) genotype-1 infections is ineffective in maintaining sustained viral response in 50% of the infection cases. New compounds in the form of protease inhibitors can complement the combination therapy. Asunaprevir is new to the drug regiment as the NS3-4A protease inhibitor, but it is susceptible to two mutations, namely, R155K and D168A in the protein. Thus, in our study, we sought to evaluate Andrographolide, a labdane-diterpenoid from the Andrographis paniculata plant as an effective compound for inhibiting the NS3-4A protease as well as its concomitant drug-resistant mutants by using molecular docking and dynamic simulations. Our study shows that Andrographolide has best docking scores of −15.0862, −15.2322, and −13.9072 compared to those of Asunaprevir −3.7159, −2.6431, and −5.4149 with wild-type R155K and D168A mutants, respectively. Also, as shown in the MD simulations, the compound was good in binding the target proteins and maintains strong bonds causing very less to negligible perturbation in the protein backbone structures. Our results validate the susceptibility of Asunaprevir to protein variants as seen from our docking studies and trajectory period analysis. Therefore, from our study, we hope to add one more option in the drug regiment to tackle drug resistance in HCV infections.