The marketing of insect-derived protein has led to the development of respective legal regulations on such insects-based foods in the European Union. Despite the interest in the area of insect-based food, European researchers have paid relatively little attention to consumer attitudes and behaviors towards such products or the factors that may affect them. Attempts undertaken so far in this respect are insufficient; therefore, there is a need to continue and expand research in this field. The present study attempts to verify the following research hypotheses: H1. Attitudes towards food containing insects are related to the attributes/characteristics of these products, care for health and the natural environment, and attitudes towards novelty (neophilic/neophobic); H2. Intentions to purchase food containing insects can be predicted based on attitudes towards food from insects, product attributes, and attitudes towards environmental health and novelties. An empirical study was conducted among university students (N = 1063) by an indirect interview method using a specially designed questionnaire, via an online platform (Computer-Assisted Web Interview, CAWI) in November 2023. The questionnaire was validated by assessing the construction validity and estimating the reliability of the scales used. The study results demonstrated that the attributes of insect-based food products can influence the positive attitudes towards them and behavioral intentions to consume them, and that the strength of the impact of health quality traits is far greater than that of the organoleptic or functional traits. A negative, statistically significant value of the correlation coefficient between neophobic attitude and intention to purchase this type of food was observed. Thus, respondents without food neophobia were characterized by a positive attitude towards the purchase of foods containing edible insects in their composition.