Let G be a group. For any a, b∈ G , the element a^-1b^-1ab is called the commutator of a and b. The commutator a^-1b^-1ab is denoted by [a, b] . If A and B are subsets of G , then [A,B] denotes the subgroup of G generated by {[a, b] | a ∈ A, b ∈ B}. The subgroup of G generated by all the commutators in G (that is, the smallest subgroup of G containing all the commutators) is called the derived subgroup, or the commutator subgroup, of G and denoted by [G,G]. In this paper, we determine the commutator subgroup G′ for groups of order 8q, where q is an odd prime.