Genetic improvement is essential to achieve increments in maize (Zea mays L.) grain yield components. It may be obtained through crosses, which enable to exploit the effects of intervarietal heterosis, allelic complementarity, as well as gene actions and effects. This study estimated the components of variance and genetic parameters (REML/BLUP) of an intervarietal diallel to select and predict the best genotypes for maize yield components. The experimental design was randomized blocks containing 60 intervarietal maize hybrids arranged in three repetitions. They were obtained through intervarietal crosses and evaluated in a diallel scheme, where 14 open-pollinated varieties were designated as parentals. Thus, 10 crosses were performed for each hybrid combination to obtain the number of seeds necessary for the competition test. The measured traits were: grain volume relative index, the mass of one hundred grains, and grain yield. The male parents and the additive genetic fraction were determinants for grain volume relative index. Mass of one hundred grains and grain yield were defined by the specific combining ability, and female parents revealed low narrow sense heritability. The female parent Taquarão and male parent Argentino Amarelo presented the best general combining abilities for the measured traits. The specific combining abilities were expressed for crosses AL 25 x Dente de Ouro Roxo, AL 25 x BRS Pampeano, and Taquarão x Argentino Branco. Genetic estimates and predictions were consistent and applicable to breeding programs and could be applied in future quantitative genetic studies of maize.