This paper deals with on the continuity of the solution to the Minkowski problem for L p torsional measure. For p ∈ (1, n + 2) ∪ (n + 2, ∞), we show that a sequence of convex bodies in R n is convergent in Hausdorff metric if the sequence of the L p torsional measures (associated with these convex bodies) is weakly convergent. Moreover, we also prove that the solution to the Minkowski problem for L p torsional measure is continuous with respect to p.