The growing use of wireless technologies in power systems has raised concerns about cybersecurity, particularly regarding GPS spoofing attacks (GSAs). These attacks manipulate GPS data, leading to modifications in the phase angle of phasor measurement units (PMUs). In this paper, a Deep-learning GPS-Spoofing Counteraction (DLGSC) algorithm is proposed, utilizing PMU data for GSA detection and PMU data correction. The algorithm incorporates a recurrent neural network (RNN) and a set of long short-term memory (LSTM) units separately, for signal correction after attack detection. Unlike existing methods that struggle with simultaneous attacks or they are static methods, DLGSC tackles these challenges by leveraging deep learning techniques. By selecting appropriate features for GSA detection, DLGSC achieves accurate results. The algorithm is evaluated on standard IEEE 14-bus and IEEE 39-bus power systems, and its performance is compared to statistical, dynamic, and Deep Learning (DL) methods in the literature. Additionally, an experimental setup is designed to validate the algorithm in a laboratory environment. Results demonstrate the easy-implementable DLGSC algorithm's satisfactory real-time performance in various scenarios, such as load variations and noise, achieving over 98% accuracy. Notably, DLGSC is cable of detecting multiple GSAs on different PMUs.