A new global navigation satellite system (GNSS) spoofing signal power control algorithm under the power constraints of receiver in acquisition phase and the subsequent control is proposed in this letter. In spoofing algorithm, constraints of successful spoofing are analyzed, objective function is constructed, the power allocation optimization algorithm based on sequential quadratic programming (SQP) is proposed, and the best scheme of spoofing is given. Experimental platform is designed to prove that compared with conventional spoofing signal high power control algorithm, the new spoofing signal power control algorithm shortens Doppler frequency fluctuation time by 72.2% and reduces the range by 75.9%. The carrier-to-noise ratio of received signal is less than the threshold of receiver, and the range of three-dimensional coordinates of ECEF is significantly reduced during spoofing signal taking over receiver, This shows that the new design of spoofing signal power control algorithm can make spoofing behavior more covert, and it will make it more difficult for target receiver to detect spoofing behavior. The designed algorithm can take over receiver stealthily with the help of jamming and then pull the positioning results, which has good feasibility and effectiveness.