We aimed to model endurance, explosive power, and muscle strength in relation to body mass index (BMI) and physical-fitness tests in Greek children aged 7-10 years old. In the present large epidemiological study, anthropometric measurements and physical-fitness tests (i.e., multistage shuttle run, vertical jump, standing long jump, small ball throw and 30-m sprint) from 141,169 children were analyzed. Age- and sex-specific normative values for physical fitness tests were expressed as tabulated percentiles using the LMS statistical method. The correlation coefficients between BMI and performances were negative and significant for both sexes (p < .01) in all physical-fitness tests. The only exception was a positive correlation between ball throw and BMI (p < .01). Only 2.9% and 4.0% of boys and girls respectively, passed the upper quartiles in all tests. The performance in speed may serve as a predictive factor explaining, at least in part, the performance in aerobic endurance and explosive power in children aged 7-10 years. The presented population-based data for physical-fitness tests revealed that only a small percentage of these children are in the upper quartiles in all tests. Furthermore, the data suggests that speed performance can be used to predict physical fitness.