As a key task in hyperspectral image processing, hyperspectral anomaly detection has garnered significant attention and undergone extensive research. Existing methods primarily relt on two prior assumption: low-rank background and sparse anomaly, along with additional spatial assumptions of the background. However, most methods only utilize the sparsity prior assumption for anomalies and rarely expand on this hypothesis. From observations of hyperspectral images, we find that anomalous pixels exhibit certain spatial distribution characteristics: they often manifest as small, clustered groups in space, which we refer to as cluster sparsity of anomalies. Then, we combined the cluster sparsity prior with the classical GoDec algorithm, incorporating the cluster sparsity prior into the S-step of GoDec. This resulted in a new hyperspectral anomaly detection method, which we called Turbo-GoDec. In this approach, we modeled the cluster sparsity prior of anomalies using a Markov random field and computed the marginal probabilities of anomalies through message passing on a factor graph. Locations with high anomalous probabilities were treated as the sparse component in the Turbo-GoDec. Experiments are conducted on three real hyperspectral image (HSI) datasets which demonstrate the superior performance of the proposed Turbo-GoDec method in detecting small-size anomalies comparing with the vanilla GoDec (LSMAD) and state-of-the-art anomaly detection methods. The code is available at https://github.com/jiahuisheng/Turbo-GoDec.