A modified HIV infection model with saturation incidence is studied. By analyzing the corresponding characteristic equations

the local stability of an infectionfree equilibrium E

0

(T

0

0

0) and a positive equilibrium E

*

(T

*

I

*

V

*

) is discussed. By using suitable Lyapunov functions and the LaSalle invariant principle

it is proved that if the basic reproductive number R

0

<

1

the infectionfree equilibrium E

0

(T

0

0

0) is globally asymptotically stable. If the basic reproductive number R

0

>

1

by means of the second additive compound matrix

the globally asymptotical stability of the positive equilibrium E

*

(T

*

I

*

V

*

) is obtained. Numerical simulations are carried out to illustrate the main theoretical results.