The most efficient breeding strategies in crop improvement is the selection based on heritability and combing ability estimates for the traits of economic importance or commercial value. Therefore, the present study was to obtain estimates of heritability and to estimate the phenotypic and genotypic correlations among the characteristics of interest. The commercial cultivars ‘Aromas’, ‘Camarosa’, ‘Dover’, ‘Festival Flórida’, ‘Oso Grande’, ‘Sweet Charlie’ and ‘Milsei-Tudla’, and 103 F1 hybrids from the crossbreeding experiments were evaluated for four traits of commercial fruit yield and 13 traits of fruit physical and chemical quality. The estimated genetic parameters were general combining ability, specific combining ability, genotypic correlation among traits, estimates of heritability, genetic and phenotypic variance. The ‘Camarosa’ and ‘Aromas’ cultivars were the most promising cultivars for use as parents in the commercial fruit production, while ‘Dover’ and ‘Sweet Charlie’ cultivars were selected for taste of fruit in strawberry breeding, as they showed higher concentrations of favorable alleles in the F1 hybrid population. It was also verified some strong genetic correlations for some pairs of characteristics in the present study that may allow indirect selection. The estimation of these parameters is an important basis for decision making on the genetic engineering of strawberry.