Let Uq (gl⊕pm) be the quantized universal enveloping algebra of gl⊕pm. Let θ be the automorphism of Uq (gl⊕pm) which is defined on generators by Ei→Ei−m, Fi→Fi−m, Kj→Kj−m for any i ∈ Z/pmZ\{0,m,..., (p-1)m} and any j ∈ Z/pmZ. Let H (p,p,n) be the Hecke algebra of type G (p, p,n) with parameters q, ε, where ε is a primitive pth root of unity. In this paper we establish a Schur–Weyl reciprocity between H (p,p,n) and a twisted tensor product of Uq (gl⊕pm) and the group algebra for θ (a cyclic group of order p) by using the results in [J. Hu, J. Algebra 274 (2004) 446-490].