HCV is a global health issue that damages the liver and is transmitted through infected blood. Many patients remain asymptomatic until the disease progresses, with treatment lasting up to six months but offering no protection against reinfection. Due to uncertainties in parameter values, we investigate a treatment strategy for HCV using a stochastic imprecise model. Our approach incorporates stochastic decision-making to optimize treatment interventions under uncertainty. We also derive estimates for the treatment control and establish necessary and sufficient conditions for the near-optimal control problem, based on the Hamiltonian function’s maximum condition and the Ekeland principle. Numerical simulations are provided to validate the theoretical results.