In this work we formulate and analyze a mathematical model for the transmission of West Nile Virus (WNV) infection between vector (mosquito) and avian population. We find the Basic Reproductive Number R0 in terms of measurable epidemiological and demographic parameters. R0 is the threshold condition that determines the dynamics of WNV infection: if R0< or =1 the disease fades out, and for R0 >1 the disease remains endemic. Using experimental and field data we estimate R0 for several species of birds. Numerical simulations of the temporal course of the infected bird proportion show damped oscillations approaching the endemic value.