Most of the evaluation indexes have the characteristics of multi-source uncertainty (MSU) because the data of them have much source, different storage mode and handling methods. It is reflected by the evaluation values including grey number, fuzzy number, interval-valued fuzzy number and white number. For the evaluation problem of such indexes, we propose a new dynamic comprehensive evaluation model of multi-source uncertain index (MSUI) based on the generalized grey incentive factors. At first, we introduce the generalized grey number and extend the traditional grey absolute correlation model to the form of evaluation indexes of generalized grey number, thus determine the generalized grey incentive factors. Then according to the characteristic of information asymmetry of indexes, we build the generalized grey entropy weight model based on the MSUI, and determine the generalized grey entropy weight of each index. Next, we build the dynamic comprehensive evaluation model of MSUI based on the generalized grey incentive factors with the generalized grey incentive factors and the generalized grey entropy weight. Finally, it proves the effectiveness and feasibility of the model through the case study.