In recent years in Western Europe, studies on entomophagy have drawn the attention of many researchers interested in identifying parameters that could improve the acceptability of insect consumption in order to introduce insects as a sustainable source of protein into the future diet. Analysing the factors involved in consumer acceptability in the Mediterranean area could help to improve their future acceptance. A cross-sectional study was conducted using an ad-hoc questionnaire in which 1034 consumers participated. The questionnaire responses allowed us to study the areas relevant to acceptance: neophobia, social norms, familiarity, experiences of consumption and knowledge of benefits. Only 13.15% of participants had tried insects. Disgust, lack of custom and food safety were the main reasons for avoiding insect consumption. Consequently, preparations with an appetising appearance need to be offered, with flours being the most accepted format. The 40–59-year-old age group was the one most willing to consume them. To introduce edible insects as food in the future, it is important to inform people about their health, environmental and economic benefits because that could increase their willingness to include them in their diet.