Objective To study the change of the roughness parameters with the surface morphologies having different height distribution functions. Methods Height distribution function (HDF) contains the height information of a surface morphology that can be reconstructed through the inverse operation of the HDF. In this paper, we calculated the amplitude roughness parameters used to characterize the different surface morphologies generated by different HDFs. Results By analyzing the correlation of these calculated parameters, it showed that some of the parameters (Ra, Rq, Rsk, Rku) may change correlatively with the shape of the HDFs. Based on the simulation results, a criterion for selecting the suitable amplitude parameters was presented. Conclusion According to the requirements, some suitable roughness parameters could be chosen for characterization of surface morphology. If the surface morphologies had the same height distribution function, they could be characterized by the parameters related either to the surface peek and valley (such as Rp, Rv) or to the height information (such as Rtm, R3y). If the surface morphologies had different height distribution functions, they could be simply distinguished by the parameters determined by the height distribution function (such as Ra, Rq, Rsk, Rku), and then the other parameters could be measured according to the requirements.