A kind of two-strain SEIJV epidemic model with two-strain and vaccination was set up. This vaccine provides complete against strain 2, but only partial against strain 1 or the vaccinated individual may be infected by strain 1. It is also assumed that strain 1 can mutate into stran 2 at a rate. The reproduction numbers of this model were given. The existence of stability of these equilibria are presented. Under certain conditions, it shows that this model exhibits have backward bifurcations.