This paper describes a non-coherent technique for fast acquisition of direct sequence spread spectrum (DSSS) signals transmitted by low earth orbit (LEO) satellites. Large Doppler offsets brought by the high speed moving LEO have become the main obstacle of the traditional acquisition methods, resulting in seriously worsen performance of acquisition. The shorter lasting time demands faster acquisition speed. This paper discusses the use of a set of partial matching filters for code phase searching in time domain, combined with a fast Fourier transform(FFT) for the purpose of parallel Doppler estimation. Compared to conventional techniques, faster code phase searching speed and a wider range of Doppler offsets can be acquired in less time. This can afford the bases for the research on DSSS signals acquisition of LEO satellites.