By broadcasting false Global Navigation Satellite System (GNSS) signals, spoofing attacks will induce false position and time fixes within the victim receiver. In this article, we propose a Sparse Decomposition (SD)-based spoofing detection algorithm in the acquisition process, which can be applied in a single-antenna receiver. In the first step, we map the Fast Fourier transform (FFT)-based acquisition result in a two-dimensional matrix, which is a distorted autocorrelation function when the receiver is under spoof attack. In the second step, the distorted function is decomposed into two main autocorrelation function components of different code phases. The corresponding elements of the result vector of the SD are the code-phase values of the spoofed and the authentic signals. Numerical simulation results show that the proposed method can not only outcome spoofing detection result, but provide reliable estimations of the code phase delay of the spoof attack.