The polymer chain growth in brushes takes place in a non-uniform environment which is one of the reasons of higher dispersity. Some active chain ends grow in monomer-reach regions while others in polymer-rich regions where the monomer concentration is lower. This effect depends on grafting density but also on the polymerization and diffusion rates. If chains grow fast, they adopt non-equilibrium conformations which change the polymer density profile and the growth conditions. In this paper we study this effect and chain relaxation using Monte Carlo simulation method. The growth of polymer brushes by living polymerization at various conditions was simulated until some average molecular weight was attained. Then, the polymerization was stopped and the changes of polymer parameters in time were monitored. The chain end-to-end distance increases and consequently the brush thickness increases in time. Polymer concentration decreases, especially near the grafted surface. The effect is stronger for higher polymerization rate and for higher grafting density. For low polymerization rates and lower grafting density, chain relaxation takes place during polymerization and the brush structure essentially does not change in time whenthe polymerization is finished. Such conditions assure also lower dispersity.