A HIV-1 epidemic model with time delay and saturation incidence rate is proposed. The global stabilities of a disease-free equilibrium E

0

(T

0

0

0) and a positive equilibrium E

+

(T

*

I

*

V

*

) are discussed. By constructing Lyapunov functions and LaSalle's invariant principle

it is shown that if dμ

>

sγβ

the disease-free equilibrium E

0

(T

0

0

0) is globally asymptotically stable

and if dμ

<

sγβ

 the positive equilibrium E

+

(T

*

I

*

V

*

) is globally asymptotically stable

for all τ≥0. Numerical simulations are carried out to illustrate the theoretical results.