With recent developments of wireless communication technologies, malicious users can use them to commit crimes or launch terror attacks, thus imposing new threats on the public security. To quickly respond to defend these attacks, authorized parities (e.g., the National Security Agency of the USA) need to intervene in the malicious communication links over the air. This paper investigates this emerging wireless communication intervention problem at the physical layer. Unlike prior studies using jamming to disrupt or disable the targeted wireless communications, we propose a new physical-layer spoofing approach to change their communicated information. Consider a fundamental three-node system over additive white Gaussian noise (AWGN) channels, in which an intermediary legitimate spoofer aims to spoof a malicious communication link from Alice to Bob, such that the received message at Bob is changed from Alice’s originally sent message to the one desired by the spoofer. We propose a new symbol-level spoofing scheme, where the spoofer designs the spoofing signal via exploiting the symbol-level relationship between each original constellation point of Alice and the desirable one of the spoofer. In particular, the spoofer aims to minimize the average spoofing-symbol-error-rate (SSER), which is defined as the average probability that the symbols decoded by Bob fail to be changed or spoofed, by designing its spoofing signals over symbols subject to the average transmit power constraint. By considering two cases when Alice employs the widely-used binary phase-shift keying (BPSK) and quadrature phase-shift keying (QPSK) modulations, we obtain the respective optimal solutions to the two Part of this paper has been submitted to the IEEE Global Communications Conference (GLOBECOM) workshop on Trusted Communications with Physical Layer Security (TCLPS), Washington, DC USA, December 4-8, 2016 . J. Xu is with the School of Information Engineering, Guangdong University of Technology (e-mail: email@example.com). He is also with the Engineering Systems and Design Pillar, Singapore University of Technology and Design. L. Duan is with the Engineering Systems and Design Pillar, Singapore University of Technology and Design (email: lingjie firstname.lastname@example.org). R. Zhang is with the Department of Electrical and Computer Engineering, National University of Singapore (e-mail: email@example.com). He is also with the Institute for Infocomm Research, A*STAR, Singapore.