In view of the inadequacy problem of most existing anomaly detection methods in effectively handling incomplete mixed data, a fuzzy multi-granularity anomaly detection algorithm for incomplete mixed data ADFIIS (Anomaly Detection in Fuzzy Incomplete Information System) was designed, which took into account the presence of missing values in both nominal and numeric attributes,and could handle mixed attribute data. The fuzzy similarity between attributes was defined and then the fuzzy entropy of each attribute was calculated. Based on the entropy values, a multi-granularity approach was employed to construct multiple attribute sequences. Subsequently,the outliers of each sample were calculated to characterize its degree of anomaly. Finally, the corresponding ADFIIS algorithm was designed, and its complexity was analyzed. Experiments were conducted on publicly available datasets, and the proposed algorithm was compared with some mainstream outlier detection algorithms such as ILGNI (Incomplete Local and Global Neighborhood Information network). Experimental results show that ADFIIS has better Receiver Operating Characteristic (ROC) curve performance on incomplete mixed datasets. On average, the Area Under the ROC Curve (AUC) of ADFIIS is better than 90% of the comparison methods. Compared with ILGNI, which can also handle incomplete mixed data, the average AUC of ADFIIS is improved by 7 percentage points. In the proposed algorithm, the model expansion method is used to detect anomalies in incomplete datasets without changing the original datasets, which expands the application scope of anomaly detection.