Abstract: Quantitative evaluation of the visual complexity of 2D logos aims at reproducing manual evaluation of logos complexity using a model based on various contributing variables. This paper presents a model capable of evaluating logo shape complexities based on regression analysis. We started from manual evaluation of logo training data, and then proposed several variables of geometric features to numerically measure logo complexities from different perspectives. Finally, we selected four variables among given 17 candidates of variables through regression analysis to obtain a model for measuring logo complexities. Experimental results show that our model is able to explain 80% of the results of logo complexity evaluated manually. The validation results of a new logo testing data set show that the Spearman correlation coefficient between the model evaluation and manual evaluation of logo testing data is 0.922（the maximum value is 1）. Potential applications of our work range from logo shape analysis, logo retrieval to logo classifications.