To solve the problem of high complexity and low computational efficiency of the coherent sound field prediction model in a closed space， a fast prediction method（FMA-ISM）of coherent sound field is proposed using the principle of image-source method （ISM） and fast multipole algorithm（FMA）. The sound source in a closed space is equivalent to a set of regularly arranged multiple source points. A virtual receiving point model based on the principle of image-source method， and a multi-point to multi-point sound field prediction model based on the coherence of the sound field are constructed. A fast multipole expansion algorithm is introduced to convert the complex mapping relationship of multi-point to multi-point into a fast calculation process of point set to point set. By reducing the order of virtual source analysis， this method improves the calculation efficiency while ensuring the accuracy of the model. The effectiveness of the method is verified by simulation and experiments. Compared with the finite element method， ray-tracing method and image-source method， the FMA-ISM method obtains smaller sound pressure level prediction error （within 3 dB） and higher calculation speed （increased by at least 50%）