A vertex-magic total labeling of a graph G=(V, E) with v vertices and e edges is an assignment of the integers from 1 to v + e to the vertices and edges of G with the property that the sum of the label on a vertex and the labels on its incident edges is a constant, independent of the choice of the vertex. In this paper we give a vertex-magic total labeling for the generalized Petersen graphs P(n, m) for all n≥3,1≤m⌊(n-1)/2⌋.