Aviation fuel efficiency is an important target for aviation industry. Aircraft engine compression ratio is a key factor to improve fuel consumption. Compression ratio can be increased using transonic compressor. In this study, performance prediction of a transonic axial compressor at design and off-design operating conditions is investigated numerically using ANSYS-CFX software. The compressor is NASA Rotor 37. Firstly, the performance at design point is predicted, where mesh independence study is performed to determine suitable mesh size. Three-dimensional flow details for meridional plane, blade-to-blade plane and airfoil surface are explored. The design point study successfully captured flow features such as shock waves and flow separation regions. When compared with experimental data, the predicted compressor pressure ratio deviation error is less than 5%. 3D flow details show that shock wave strength increases from hub to tip. The shock wave moves backward as we move from hub to tip indicating that the flow separation covers lesser portion of the blade. Secondly, off-design performance is predicted for various rotational speeds. A simple procedure is utilized to predict surge and choke limits. The predicted compressor map is compared with experimental data and it shows overall root mean square error less than 5%. The success of the method developed in this research make it a viable method to be used in the design phase of transonic compressors to evaluate the effect of design modifications for both design and off-design operating conditions.