Well conditions during drilling operation can be predicted using numerical simulation. During under-balanced drilling (UBD) operation, controlling the bottom-hole pressure (BHP) in a suitable range and also appropriate hole-cleaning is essential. In this paper, numerical simulation of gas-liquid-solid three-phase flow in the annulus is used to study the effects of annulus geometry and also liquid properties on the BHP and hole-cleaning during UBD operation. To validate the numerical simulation, the results are compared with the experimental data from a laboratory study. Also, the gain results from developed code are compared with the actual field data from a real well, several mechanistic models from WellFlo software, and gas- liquid two- fluid numerical simulation. Due to the significance of controlling the BHP and hole-cleaning during UBD operation, the effects of annulus geometry and liquid phase properties on BHP and the solid volume fraction distribution are investigated. According to the results, changing the hydraulic diameter and cross-sectional area of the annulus can affect BHP and hole- cleaning in UBD operation. In other words, increasing the hydraulic diameter at a constant cross- sectional area improves hole-cleaning and decrease BHP. Also, decreasing the cross-sectional area at a constant hydraulic diameter improves hole-cleaning and increase BHP. The results show that the liquid viscosity affects hole-cleaning through two contrary mechanisms. In fact, by increasing the liquid viscosity, carrying capacity of the liquid phase is increased and cutting transfer velocity is decreased.