The spoofing attack is critical to bypass physical-layer signal authentication. This paper presents a deep learning-based spoofing attack to generate synthetic wireless signals that cannot be statistically distinguished from intended transmissions. The adversary is modeled as a pair of a transmitter and a receiver that build the generator and discriminator of the generative adversarial network, respectively, by playing a minimax game over the air. The adversary transmitter trains a deep neural network to generate the best spoofing signals and fool the best defense trained as another deep neural network at the adversary receiver. Each node (defender or adversary) may have multiple transmitter or receiver antennas. Signals are spoofed by jointly capturing waveform, channel, and radio hardware effects that are inherent to wireless signals under attack. Compared with spoofing attacks using random or replayed signals, the proposed attack increases the probability of misclassifying spoofing signals as intended signals for different network topology and mobility patterns. The adversary transmitter can increase the spoofing attack success by using multiple antennas, while the attack success decreases when the defender receiver uses multiple antennas. For practical deployment, the attack implementation on embedded platforms demonstrates the low latency of generating or classifying spoofing signals.