Green low-carbon port (GLCP) development and evaluation have gained increase attention in recent years. However, the uncertain assessment procedure and complex index in the GLCP assessment has brought great challenges to achieve a consensus for decision. To solve above problems, this study aims to present a novel decision making framework based on Fermatean fuzzy integrated weighted distance measure and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) approach for the GLCP evaluation. The Fermatean fuzzy integrated weighted average distance (FFIWAD) measure is first proposed, which takes into account the subjective significance of the variables and the attitudinal characteristics of decision makers. A FFIWAD-TOPSIS decision making framework is then developed, wherein the weights of index are determined by entropy method, and the FFIWAD is applied to calculate the distance between each alternative and the positive (or negative) ideal solution. Moreover, on the basis of the constructed index system of GLCP evaluation, the presented FFIWAD-TOPSIS method is applied to assess the development status GLCP of five major ports in China. The case analysis shows that Guangzhou Port behaves the best comprehensive performance among the five cities, while Shenzhen Port is the worst. Finally, the sensitivity analysis, as well as comparative analysis of the presented model are conducted.