In this paper, gas-liquid two-phase flow in the annulus of a real well during under-balanced drilling operations is simulated numerically. Oil and gas flow from the reservoir in to the annulus is considered due to under-balanced drilling condition. A numerical code based on one-dimensional form of steady-state single pressure two-fluid model in the Eulerian frame of reference is developed and its results are validated using experimental data from two real wells. The results of numerical simulation show better accuracy in comparison with other researches. Given the importance of prediction and control of the bottom-hole pressure and the amount of oil and gas production during the drilling operations, the effects of controlling parameters such as liquid and gas injection flow rate and choke pressure are discussed. Also, the effects of different controlling parameters on the characteristics of two-phase flow pattern, including liquid and gas void fractions, liquid and gas velocities and pressure distribution along with the annulus are discussed. According to the results, the effects of choke pressure and injected liquid flow rate on the production of the oil from the reservoir are independent of the values of each other and are dependent on the injected gas flow rate.