Air travel is growing at an alarming rate. However, according to the latest research report by Eurocontrol on European aviation, the growth of air traffic will be limited by the available spectrum resources. As one of the means to provide air/ground (A/G) broadband communication, the L-band digital aeronautical communication system (LDACS) is becoming the preferred model for final deployment and has received continuous attention. Based on various spectrum measurement studies, the international civil aviation organization (ICAO) has identified multiple 1 MHz vacant bands between adjacent distance measuring equipment (DME) signals for LDACS. In order to improve spectrum efficiency, the concept of dynamic spectrum access (DSA) can be applied to the LDACS, which requires the use of spectrum sensing methods to detect the spectrum holes of DME users. In this paper, an adaptive threshold energy detection spectrum sensing method is proposed based on the characteristics of DME pulse signals. Firstly, the energy of the received signal is estimated to construct the detection statistics, and the equations of detection probability and false alarm probability are established. Secondly, the adaptive threshold is calculated using the maximum likelihood decision criterion under the assumption of a constant probability of false alarm. Thirdly, the detection statistic is compared to the adaptive threshold to determine the spectrum occupancy state in the decision-making stage. Finally, the result is transmitted back to the transmitter for the best spectrum resource allocation. According to the simulation analysis, the adaptive threshold energy detection-based sensing method outperforms the energy-difference detection method under low signal-to-noise ratio (SNR) conditions. Meanwhile, it has superior adaptability since the adaptive threshold can be adaptively changed according to the channel.