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Hepatitis C is a viral infection that appears as a result of the Hepatitis C Virus (HCV), and it has been recognized as the main reason for liver diseases. HCV incidence is growing as an important issue in the epidemiology of infectious diseases. In the present study, a mathematical model is employed for simulating the dynamics of HCV outbreak in a population. The total population is divided into five compartments, including unaware and aware susceptible, acutely and chronically infected, and treated classes. Then, a Lyapunov-based nonlinear adaptive method is proposed for the first time to control the HCV epidemic considering modelling uncertainties. A positive definite Lyapunov candidate function is suggested, and adaptation and control laws are attained based on that. The main goal of the proposed control strategy is to decrease the population of unaware susceptible and chronically infected compartments by pursuing appropriate treatment scenarios. As a consequence of this decrease in the mentioned compartments, the population of aware susceptible individuals increases and the population of acutely infected and treated humans decreases. The Lyapunov stability theorem and Barbalat's lemma are employed in order to prove the tracking convergence to desired population reduction scenarios. Based on the acquired numerical results, the proposed nonlinear adaptive controller can achieve the above-mentioned objective by adjusting the inputs (rates of informing the susceptible people and treatment of chronically infected ones) and estimating uncertain parameter values based on the designed control and adaptation laws, respectively. Moreover, the proposed strategy is designed to be robust in the presence of different levels of parametric uncertainties.