In the future an approach incorporating cows’ measured phenotypes and marker genotypes of cows and bulls within a single model can be applied. The most important advantage of such a model is the simultaneous use of pedigree and marker-based genomic relationship data. Such a solution allows the use of both genotyped and non-genotyped animals in the prediction procedure. This pilot study is aimed towards implementation of a one-step approach in a random regression test day model context for the Polish Holstein Friesian population, considering various ways of adjusting the relationship matrix. Data consisted of 890 animals (10 genotyped bulls, 100 cows with phenotypic data and 780 ancestors without genotypes or phenotypes). Random regression test day models with a polygenic effect on milk yield modeled by second order Legendre polynomials for the estimation of variance-covariance parameters and were used for prediction of genomically enhanced breeding values (GEBV). In this model, a matrix combining pedigree and marker-based information was used instead of a traditional numerator relationship matrix. In this matrix the proportions of information coming from pedigree and markers were defined by weighting parameters w and 1-w for pedigree and marker-based information matrices, respectively. Various weights of the two sources of information were considered. The accuracy of GEBV both for genotyped bulls and for cows with phenotypes was highest for weighting parameter w=0 and lowest for w=l. Incorporating genomic information into a conventional genetic evaluation improves reliabilities of breeding value prediction, however, pedigree information is important to maintain the stability of evaluation for non-genotyped animals. Implementation of the single-step approach in a random regression test day model framework is very attractive for genomic prediction in dairy cattle, since it allows to incorporate genomic information directly into a conventional genetic evaluation. However, for accurate predictions it is essential to achieve the right balance between the numerator relationship and markers-based relationship information.