Hepatitis C virus infection is one of the severe hepatological issues due to its life-threatening potentiality. In this paper, we proposed and analyzed a mathematical model to study the transmission dynamics of chronic hepatitis C virus (HCV) infection consisting of infected and uninfected hepatocytes as well as HCV-specific cytotoxic T cells through a coupled system of differential equations. The chronicity of infection is linearly dependent to duration of infection stages leading the infection to liver cirrhosis and hepatocellular carcinoma. The basic reproduction number ( \(R_0\) ) provides conception about the persistence and eradication of the infection. The system also experiences transcritical bifurcation for \(R_0 = 1\) . To perform the robustness of the system with respect to the model parameters, we conduct a normalized forward sensitivity analysis. Additionally, a discrete time lag is taken into account in the phase where formation of efficient infected hepatocytes alternated from latently infected hepatocytes takes place. The model analysis carries out that in spite of fluctuations in cell population, endemic steady state is asymptotic stable for all delay. Numerical simulation is accomplished with biological significances to validate analytical results.