The complete binary tree as an important network structure has long been investigated for parallel and distributed computing, which has many nice properties and used to be embedded into other interconnection architectures. The Mobius cube M-n is an important variant of the hypercube Q(n). It has many better properties than Qn with the same number of edges and vertices. In this paper, we prove that the complete binary tree with 2(n) - 1 vertices can be embedded with dilation 1, congestion 1, load 1 into Mn and expansion tending to 1. (C) 2015 Elsevier Inc. All rights reserved.