Weak global navigation satellite system(GNSS) signal acquisition has been a limitation for high sensitivity GPS receivers. This paper modifies the traditional acquisition algorithms and proposes a new weak GNSS signal acquisition method using re-scaling and adaptive stochastic resonance(SR). The adoption of classical SR is limited to low-frequency and periodic signals. Given that GNSS signal frequency is high and that the periodic feature of the GNSS signal is affected by the Doppler frequency shift, classical SR methods cannot be directly used to acquire GNSS signals. Therefore, the re-scaling technique is used in our study to expand its usage to high-frequency signals and adaptive control technique is used to gradually determine the Doppler shift effect in GNSS signal buried in strong noises. The effectiveness of our proposed method was verified by the simulations on GPS L1 signals. The simulation results indicate that the new algorithm based on SR can reach-181 d BW sensitivity with a very short data length of 1 ms. Weak global navigation satellite system (GNSS) signal acquisition has been a limitation for high sensitivity GPS receivers. This paper modifies the traditional acquisition algorithms and proposes a new weak GNSS signal acquisition method using re-scaling and adaptive stochastic resonance (SR). The adoption of classical SR is limited to low-frequency and periodic signals. Given that GNSS signal frequency is high and that the periodic feature of the GNSS signal is affected by the Doppler frequency shift, classical SR methods can not be directly used to acquire GNSS signals. , the re-scaling technique is used in our study to expand its usage to high-frequency signals and adaptive control technique is used to determine the Doppler shift effect in GNSS signal buried in strong noises. The effectiveness of our proposed method was verified by the simulations on GPS L1 signals. The simulation results indicate that the new algorithm based on SR can reach-181 d BW sensitivity with a very short data length of 1 ms.