In multi-attribute group decision making (MAGDM), it is important to deal with heterogeneous data and integrate the evaluation information from different decision makers (DMs). To more accurately capture the uncertain information in the real decision-making environment, a hybrid MAGDM method using normal cloud model (NCM) and multi-granularity information is proposed. First, utilizing the theta scaling method, multi-granularity linguistic term sets are established. Considering the exact numbers, interval numbers, multi-granularity linguistic terms, and multi-granularity linguistic expressions, the concept of multi-granularity information is further expanded. Second, these data with different granularity are uniformly converted into NCMs, which can simultaneously preserve both magnitude information and uncertainty information. Third, based on the internal consensus index (ICI) and the external consensus index (ECI), a novel group analytic hierarchy process (GAHP) method is proposed for calculating attribute weights. Finally, NCM-extended VIKOR method is proposed for ranking the alternatives. The flexibility and superiority of the proposed method are confirmed through a case study and comparisons with previous methods.