The mutual range-join of k sets, S1, S2, . . , S4, is the set containing all tuples (s1, s2, . ., st) that satisfy e, I 1 si -s, 1 I e, for all 1 I i +j I k, where si E Sj and e, 5 e2 are fixed constants. This paper presents an efficient parallel algorithm for computing the k-set mutual range-join in hypercube computers. The proposed algorithm uses a fast method to determine whether the differences of all pair numbers among k given numbers are within a given range and applies the technique of permutation-based range-join [ll]. To compute the mutual range-join of k sets S,, S,; . . , S, in a hypercube of p processors with 0(X;, ,n;/p) local memory, p < 1 Si 1 = n, and 1 < i 5 k, our algorithm requires at most O((k log k/pN-I& ,_ ,ni) data comparisons in the worst case. The algorithm is implemented in PVM and its performance is extensively evaluated on various input data.