The study of quaternion CR-submanifolds, i.e., submanifolds of an almost quaternion Hermitian manifold which admit a differentiable quaternion distribution such that its orthogonal complementary distribution is totally real, was initiated in 1981 in Barros et al. (Kodai Math J 4, 399–417, 1981). In Barros and Urbano (Boll Un Mat Ital A (6)2(1): 103–110, 1983), the authors prove that under certain conditions a quaternion CR-submanifold of a Euclidean space has the homotopy type of a CW complex and they also state some results on the cohomology of a quaternion CR-submanifold.