A novel GPS initial synchronization scheme with low hardware complexity is proposed. The proposed method has the decomposed differential matched filter, which consists of 25% multiplier and adder of the conventional matched filter. This paper presents the generalized mean acquisition time of initial synchronization scheme with multiple correlator. It is shown that the proposed method, in spite of its low hardware complexity, has the equal performance to the conventional method. The performance of the proposed method is verified through the simulation test by the GPS simulator. It is shown that the proposed method prevents the squaring loss of non-coherent integration.