With the widespread application of GNSS systems in various fields, the problem of spoofing detection has drawn much attention from the satellite navigation community. The GNSS spoofing interference generally uses fake or replayed satellite signals to make the targeted receivers receive false GNSS signals and reduce the accuracy of calculated position and time information. In order to ensure and improve the security of GNSS services, in recent years, academia and industry have studied the spoofing detection technology from multiple aspects, and many theoretical results have been obtained. This paper starts the analysis from the acquisition phase of a receiver and analyzes the characteristics of the small-delay spoofing signal. Aiming at solving the problem that it is difficult to detect small-delay (0-2 chips) spoofed signals during the acquisition phase, the CNN (Convolutional Neural Network) based method is used to detect the small-delay spoofed signals effectively. According to the experimental simulation results, when the code phase difference between the spoofing signal and the authentic satellite signal is larger than 0.5 code chip, the CNN-based method achieves high detection accuracy. In addition, the algorithm can quickly detect the data without using any additional equipment. Therefore, low complexity is achieved. This makes the algorithm has a good engineering application prospect.