By using the method of constructing some convex functional

the existence of positive solution for p-Laplacian difference equations is considered.By mean of the corresponding difference operator and appropriate convex functional

the new sufficient conditions of at least a positive solution existence for this kind of boundary value problem are established.The given conditions only relate to the properties of the nonlinear term on bounded sets

without the assumptions of superlinearity

sublinearity or lower and upper solutions.The results are illustrated with an example

and extend and improve some known results.