The key factors in overcoming for weak global navigation satellite systems (GNSS) signal acquisition are sensitivity and dwell time. In the conventional MAX/TC criteria, a preset threshold value is used to determine whether the signal exists. Thus the threshold is calculated carefully to balance the sensitivity and the dwell time. Affected by various environment noise and interference, the acquisition circuit will enter verifying mode frequently to eliminate false alarms, which will extend the mean acquisition time (MAT). Based on the periodicity of spread spectrum code in GNSS, this paper presents an improved double-dwell scheme that uses no threshold in detecting weak GNSS signals. By adopting this method, the acquisition performance of weak signal is significantly improved. Theoretical analysis and numerical simulation are presented detailed. Compared with the conventional MAX/TC criteria, the proposed method achieves improved performance in terms of detection probability and false alarm rate. Furthermore, the MAT decreases 15s when C/N₀ is above 20dB-Hz. This can enhance the receiver sensitivity and shorten the time to first fix (TTFF).