Genetic parameters, which are based upon (co) variance components, are necessary elements in dairy cattle genetic evaluation programmes for either productive or reproductive traits that are of economic importance. Recently, there has been an increasingly interest in applying Bayesian-based methods as an alternative over classical linear models such as REML to estimate more accurate genetic parameters of the traits under consideration in animal breeding data (Gianola, 2000). However, as compared to classical methods such as REML, Bayesian estimation of genetic parameters is theoretically more complex and also needs much more computational time that could be a potential a limiting factor in practical application of the Bayesian methods. In this study the main objective is to estimate of heritability of complete lactation milk yield of Iranian Holstein heifers with the use of Bayesian (based on Gibbs Sampling that is a Monte Carlo method) and REML (based on Analytical Gradients technique) approaches.