Abstract: The tiered spreading code, which is widely adopted in the new generation of satellite navigation system, brings an obstruction for signal acquisition. This paper investigates the cascade FFT(Fast Fourier Transform) algorithm applied to the joint acquisition of tiered spreading code signal. The mathematic representation of the algorithm is derived for the first time and provided as theory foundation for the algorithm. The acquisition performance affected by carrier Doppler effect and code Doppler shifts are demonstrated via analysis in detail, according to the mathematic representation. The influence caused by carrier Doppler Effect is a combined action of the residual Doppler, which results from the two steps of carrier Doppler compensation. The influence caused by code Doppler shifts leads the acquisition unsuccessful in the weak signal condition. A modified method using segment code Doppler correction is proposed, which is according to the characteristics of the code Doppler shifts and cascade FFT algorithm. The modified method can extend the total accumulation interval and reduce the integral loss. Simulations results are provided at last in the paper, which are in accordance with the performance obtained by mathematic analysis. In addition, simulations results shows that the proposed modified techniques can work effectively in the weak signal condition.