The aim of our study was to assess nutritional intake and anthropometric statuses in schoolchildren to subsequently determine nutritional adequacy with Spanish Dietary Reference Intake (DRIs). The ANIVA study, a descriptive cross-sectional study, was conducted in 710 schoolchildren (6–9 years) in 2013–2014 in Valencia (Spain). Children’s dietary intake was measured using 3-day food records, completed by parents. Anthropometric measures (weight and height) were measured according to international standards, and BMI-for-age was calculated and converted into z-scores by WHO-Anthro for age and sex. Nutrient adequacy was assessed using DRI based on estimated average requirement (EAR) or adequate intake (AI). Pearson’s chi-square and Student’s t-test were employed. Of our study group (47.61% boys, 52.39% girls), 53.1% were normoweight and the weight of 46.9% was inadequate; of these, 38.6% had excess body weight (19.6% overweight and 19.0% obesity). We found intakes were lower for biotin, fiber, fluoride, vitamin D (p < 0.016), zinc, iodine, vitamin E, folic acid, calcium and iron (p < 0.017), and higher for lipids, proteins and cholesterol. Our results identify better nutritional adequacy to Spanish recommendations in overweight children. Our findings suggest that nutritional intervention and educational strategies are needed to promote healthy eating in these children and nutritional adequacies.