The distribution of pedunculate oak in Bosnia and Herzegovina is important in connecting the southern and eastern provenances of the Balkan Peninsula with provenances from Central Europe. However, due to over-exploitation, pedunculate oak is almost extinct in Bosnia and Herzegovina. This research aims to determine the heredity and production potential of the pedunculate oak from 28 provenances in the Bosnian-Herzegovinian provenance test through the genetic gain of thickness and height growth. The results will be used in selection of best provenances in terms of genetic gain. For this research, height and root collar diameter of pedunculate oak plants in Bosnian-Herzegovinian provenance tests were measured in 2012, 2016 and 2020. The provenance test was established in 2009. It contains 28 provenances from Bosnia and Herzegovina. Heredity and selection differential were assessed using analysis of variance. Possible genetic gain if using five best and one best provenance were determined. The results of the genetic gain for height obtained using data from 2012 and 2020 were low. The results obtained for 2016 indicate that the genetic gain for height, using five best provenances would be 7.62%, and using the best provenance 9.98%. Results of the genetic gain for root collar diameter obtained for 2016 and 2020 were low. For 2012, the genetic improvement using five best provenances would be 4.28%, and using the best provenance 6.32%. The results indicate that by selecting the best provenances of pedunculate oak and their propagation, we can achieve a significant increase in plant height and thickness, i.e., the yield of wood mass. As research concerns juvenile material, it is necessary to continue systematic monitoring, to determine the actual heredity and genetic age, when the trees reach their physiological maturity, and when the annual value oscillations become uniform.