Food neophobia has been defined as the reluctance to try new foods. Food neophobia is common in children and older people, but until now, scarce research has been carried out on food neophobia in the adult population. The aim of this study was to assess the most usual food neophobias in Spanish adults with overweight and obesity by sex, and their association with sociodemographic factors and the most prevalent chronic diseases. A cross-sectional observational study was carried out on adults (mean age of 43.5 ± 13.7 years old; = 590; 50% female) with overweight or obesity. Their anthropometrics, adherence to the Mediterranean diet, age, educational level, economic level, smoking and sleeping habits, physical activity, chronic diseases, and food neophobias were assessed. The highest food neophobias in Spanish adults with overweight or obesity were directed toward vegetables, meat, fish, pulses, game meat, and fruits, mostly among females, with differences between sexes. Phobias of the soft texture of foods were also observed, without differences between sexes. Age, educational level, sleeping habits, and physical activity were directly related, and economical level and smoking were inversely related to food neophobia, mainly to healthy foods, and more obvious in males than in females. There were associations between body mass index (BMI) and chronic diseases and food neophobia. Adherence to the adaption of healthy and sustainable diets is low within food neophobics, increasing the risk of diet-related chronic diseases.