In this paper, a new model-order reduction (MOR) approach is presented for reducing large-scale differential-algebraic equation (DAE) systems with higher index. This approach is based upon the balanced truncation, single-point, and multi-point MOR methods. We decompose the DAE system into an ordinary differential equation (ODE) subsystem and a DAE subsystem. The DAE subsystem has the same index as the original DAE system. Then, the balanced truncation method is applied to the ODE subsystem. Both single-point and multi-point methods are used to reduce the DAE subsystem. In generally, the multi-point method can perform better than the single-point method across a wide-range of frequencies. Some numerical examples demonstrate the effectiveness of our approach. (C) 2013 Elsevier Ltd. All rights reserved.