The objectives of the present work were to evaluate the precision of the estimate of heritability, which was determined by standard error, considering a Bayesian approach, and to compare such estimate with the classic procedure. Data from progeny trial of 39 Eucalyptus cladocalyx families were used. Trunk basal diameter (measured at age 6) was the dependent variable analyzed. The Bayesian approach was implemented by using the Independence Chain algorithm with informative priors, which had a lower standard deviation of the heritability than both the classic method of Robertson and Jeffreys' prior distribution (Jeffreys' prior is in fact a class of uninformative and often improper prior distributions). The Bayesian approach is a valuable inference tool for the genetic evaluation of perennial species, because it considers the variability of the parameters by using posterior distributions.