The difficulties of multi-attribute decision making with interval-type attribute values and weights lie in the precision work of uncertain weight information and the ordering of interval numbers. The idea of using the approach degree to approach the ideal solution in the grey entropy model can not only avoid the troublesome steps of precising fuzzy data in multi-attribute decision making, but also can effectively solve the problem of local correlation. Considering that the traditional grey entropy model is only applicable to the situation where the attribute values are all exact real numbers and index weights are lacked, the grey relation entropy is introduced into the traditional grey entropy model to construct the grey entropy model with interval weights and attribute values, which successfully solves the problem of precising uncertain data. In order to solve the difficult problem of ordering interval numbers, this model makes the two derived variables approach the ideal solution again based on the TOPSIS method to calculate the degree of balance and approach to sort the solution. Finally, the effectiveness of the model is verified by the example of SG laser device project in selecting a non-standard component supplier.