The aims of the present study were to estimate genetic parameters, as well as phenotypic, genetic and environmental trends for milk yield (MY), lactation length (LL), fat yield (FY) and fat content (FC) on Gyr dairy breed, using a multivariate derivative-free restricted maximum likelihood (MTDFREML) with an animal model. The mathematical model included herd-year of calving, calving season, and age of cows as fixed effects, and animal, permanent environmental and error as random effects for milk yield, lactation length, fat yield and fat content. Through the bivariate analysis, estimates of heritability for productive characteristics were, respectively: MY and LL, 0.21 and 0.11; MY and FY, 0.22 and 0.21; MY and FC, 0.19 and 0.12. The estimates of repeatability were: MY, 0.51; LL, 0.32; FY, 0.47; and FC, 0.13. The phenotypic, genetic and environmental correlations for productive characteristics were, respectively: MY and LL, 0.62, 0.76 and 0.57; MY and FY, 0.93, 0.97 and 0.91; MY and FC, –0.02, –0.11 and –0.01. The annual phenotypic, genetic and environmental trends for MY were positives with the following values, respectively: 66.93± 7.06 (P<0.01), 10.46± 1.08 (P<0.01) and 56.47 kg/year, by cows’ breeding values, and 29.63± 14.34 (P<0.05), 19.29± 5.27 (P<0.01) and 10.34 kg/year, by bulls’ breeding values. The annual phenotypic, genetic and environmental trends for LL were, respectively: –0.16± 0.31 (P>0.05), 0.21± 0.09 (P<0.05) and –0.37 days/year, by cows’ breeding values, and –0.69± 0,44 (P>0.05), –0.10± 0.28 (P>0.05) and –0.59 days/year, by bulls’ breeding values. The annual phenotypic, genetic and environmental trends for FY were, respectively: 3.53± 0.58 (P<0.01), 0.40± 0.09 (P<0.01) and 3.13 kg/year, by cows’ breeding values, and 1.37± 0.95 (P>0.05), 0.47± 0.29 (P>0.05) and 0.90 kg/year, by bulls’ breeding values. The annual phenotypic, genetic and environmental trends for FC were positive with the following values, respectively: 0.039± 0.014 (P<0.05), 0.001± 0.001 (P>0.05) and 0.038 %/year, by cows’ breeding values, and 0.010± 0.011 (P>0.05), 0.000± 0.003 (P>0.05) and 0.010%/year, by bulls' breeding values.