A graph X is said to be strongly distance-balanced whenever for any edge uv of X and any positive integer i, the number of vertices at distance i from u and at distance i+1 from v is equal to the number of vertices at distance i+1 from u and at distance i from v. It is proven that for any integers k≥2 and n≥k 2 +4k+1, the generalized Petersen graph GP(n,k) is not strongly distance-balanced.