A new functional food-labeling system was implemented in 2015. Food products with new functional information are expected to increase along the increase of health awareness in Japan. However, it is difficult for ordinal consumers to understand each functional component of food. When descriptions on food include scientific information,people often misunderstand or excessively expect about a new function. This research investigated how understanding the information of foods was correlated with individual’s cognitive traits conducting a web-based survey using a fictional news report based on real research to two groups, ordinal consumers group and specific occupations group that supposed to have high recognition degree of new functional food-labeling system. We also used three cognitive indices, the cognitive reflection test, numeracy and graph literacy, to investigate the influence of cognitive traits on reading comprehension and interpretation. The results revealed that graph literacy was correlated with understanding and that the other two indices were correlated with psychological factors of interpretation though there was no group difference.