The increase of maize yield is possible by increasing either the cultivated area, use of best technologies and also more productive genotypes. So, the aim of this study was to estimate the variance components and genetic parameters (individual REML), phenotypic linear correlations, genetic, environmental and canonical for agronomically important traits in maize. The experiments were conducted in the growing seasons of 2013/2014 in four environment of Rio Grande do Sul, Brazil. The design used was a randomized block arranged in a factorial design, including 79 maize of hybrids (simple/narrow genetic base) × four cultivation environments, arranged in three replicates. The measured traits were plant height, insertion ear height, prolificacy, ear diameter, ear length, number of grain rows per ear, number of grain per row, stem diameter, stem mass, ear mass, grains weight per ear, hundred grains weight and grains yield. The estimates of the variance components and genetics parameters (REML) were made throught the MHPRVG method, obtaining the genotypic variance, the variance of genotype × environment interaction, residual variance, individual phenotypic variance, heritability with broad sense to the total phenotypic effects, heritability of the genotypes mean, accuracy for the selection of the genotypes,determination coefficient to the effects of genotype × environnment interaction, genotypic correlation between performance of the environment, coefficient of genotypic variation,coefficient of residual variation and a overall average. We created a linear phenotypic, genetics, environmental and a canonical correlation. The variance components and genetics parameters (REML) identified a contribuition of the genetic variation for genotype × environment interaction, and heritability in a broad sense for the ear diameter, number of grains row and stem diameter. Phenotypic, genetic and environment linear positive trends was presented between the prolificacy as ear diameter and the grains mass per ear with the grain yield. The three canonical pairs were significant with intergroup dependence, by which the grains yield favored by the plant height, insertion ear height, prolificacy, ear diameter and number of grains per row. The criteria established by this study can be used in quantitative genetics research and maize genetic improvement to increase grain yield.