Step meandering during the growth of gallium nitride crystal is studied on using kinetic Monte Carlo method. Cause of instability is identified to be the particle advection caused by the step flow. Growth process is conducted in N-rich conditions and GaN(0001) surface kinetics is modeled by setting jump probabilities for Ga atoms adsorbed at the surface. We show that at low enough temperatures and relatively high external particle fluxes periodic regular pattern of meanders is created with its wavelength inversely proportional to the particle flux. An increase of the meander amplitude saturates after some period and further crystal grow is stationary, creating "finger-like" structure. For medium fluxes regular structure of meanders builds up for low or zero value of Schwoebel barrier. For higher fluxes wavelengths of meanders become shorter than the terrace width and they start to grow independently and finally transfer the surface to a rough structure. For very low fluxes or at relatively high temperatures steps move steadily remaining their initial shapes of straight, parallel lines. (C) 2012 Elsevier B.V. All rights reserved.