The acquisition is the most time-consuming step performed by a Global Navigation Satellite System (GNSS) receiver. The objective is to detect which satellites are transmitting and what are the phase and Doppler frequency shift of the signal. It is the step with the highest computational complexity, especially for signals subjected to large Doppler shifts. Improving acquisition performance has a large impact on the overall performance of the GNSS reception. In this paper, we present a two-step Global Positioning System (GPS) acquisition algorithm whose first step performs an incremental correlation to find a coarse pair of phase and frequency and the second step, triggered by the variance of the largest correlation values, refines the first step. The proposed strategy, based on the conventional time-domain serial algorithm, reduces the average execution time of the acquisition process to about 1/5 of the conventional acquisition while keeping the same modest logic hardware requirements and slightly better success and false-positive rates. Additionally, the new method reduces memory usage by a factor that is proportional to the signal’s sampling frequency. All these advantages over conventional acquisition contribute together to significantly improve the overall performance and cost of GPS receivers.