In this research work, we present an exciting mathematical analysis of a stochastic model, using a standard incidence function, for infectious disease hepatitis C transmission dynamics. In this model, we divided the infected population into three different classes with two different infection stages known as chronic class and acute class while the third is an isolation class. We also presents briefly the Legendre spectral method for the numerical solution to the proposed model. It is observed that the disease-free equilibrium is asymptotically stable, when basic reproduction number It is also shown that the proposed model has a stable endemic equilibrium when the reproduction number Also, sensitivity analysis is carried out to study and identify the effect of parameters on . Moreover, we have performed numerical simulations to study the influence of disease free equilibrium and endemic equilibrium. Legendre polynomial and Legendre weight function are used to solve the proposed stochastic system numerically. Numerical results are compared against the basic reproduction number.