It is well known that some global navigation satellite system (GNSS) signals operate on the aeronautical radionavigation services (ARNS) frequency band, which is also utilized by other aeronautical service signals, such as pulsed signals from the distance-measuring equipment (DME) system. Thus, the high-power DME signal, as interference, will significantly degrade the performance of the GNSS. Some algorithms, including time blanking, frequency notch filtering, and hybrid filtering, have been proposed to suppress DME interference. However, when the density of the DME pulse is high, they will bring a huge loss of the desired satellite signal. This paper proposes a hybrid approach for DME interference suppression by combining a novel parametric algorithm and the wavelet-packet-based algorithm. An overlap detection algorithm is also proposed to automatically switch between the two algorithms. When there is no overlapped pulse, the parametric method will be utilized to suppress the interference and retain more of the desired satellite signal. For overlapped DME pulses, the interferences are suppressed by the wavelet-packet transformation algorithm. The problem of parameter selection for wavelet-packet transformation is also discussed systematically. The trade-off between performance and complexity is obtained by adaptively selecting between the traditional algorithm and the proposed hybrid approach based on a pulse density detection algorithm. Numerical results are presented to demonstrate the effectiveness of the proposed approach.