Hepatitis C virus (HCV) is one of the leading known causes of liver disease in the world. The HCV is a single-stranded RNA virus. The genomes of HCV display significant sequence heterogeneity and have been classified into types and subtypes. Types from 1 to 11 have so far been recognized, each type having a variable number of subtypes. It has been confirmed that 90% approximately of the isolates HCV infections in Egypt belong to a single subtype (4a) [10]. In this paper, we construct a mathematical model to study the spread of HCV-subtype 4a amongst the Egyptian population. The relation between HCV-subtype 4a and the other subtypes has also been studied. The values of reproduction numbers R01, R02 have been derived [5]. Also, threshold conditions for the value of the transmission rates k1 and k02, in terms of R01, R02 and the mutation factor μ have been determined to insure that the disease will die out. If the conditions fail to happen the disease takes off and becomes endemic.