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To study the multipath channel, which contains additive colored noise, in the chirp spread spectrum system, an efficient and fast algorithm was proposed to estimate multipath delay. Firstly, the impulse compress property of the chirp signal is used to obtain a cursory estimation. Subsequently the fourth-order cumulant matrix is decomposed by MSWF to calculate the number of multipath. The final estimation of multipath delay was calculated by the decorrelation MUSIC algorithm. In the last sections, a simulation which uses the channel of IEEE 802.15.4a as a transmit environment is introduced to testify the feasibility of the new algorithm. The algorithm proposed in this paper has high precision and low computational complexity.