Abstract: The existence of positive solutions of p -Laplacian boundary value problems is studied on the semi-infinite interval. After studying the existence of positive solutions on the base of fixed point theorem of p -Laplacian operator boundary value problems on the finite interval, the interval can be extended applying the Arzela-Ascoli theorem from the finite to the semi-infinite interval. So the conclusion is found about the existence of positive solutions of p -Laplacian boundary value problems on the semi-infinite interval.