Numerical investigation of the unsteady flow patterns around the bucket can be helpful to improve the Pelton turbine efficiency. In fact, by studying the loss mechanisms in the flow, one can optimize the bucket design. For this purpose, an accurate investigation of the water jet is also necessary as an inlet condition for the bucket flow. The water jet ejected from the nozzle is actually non-uniform, due to the upstream turbulence and secondary flow in the distributor, bending pipes, needle and supports. This non-uniformity causes a deviation of the water jet from the ideal jet center, which is tangent to the jet circle, and it directly affects the flow patterns around the bucket. Whereas water splashing makes experimental observations very challenging, a numerical approach is effective and convenient to study the unsteady flow pattern in a Pelton turbine. In the present research, numerical analysis of the two-phase flow through the distributor, bending pipe and nozzle, has been performed. The jet velocity profile has been verified with experimental results, which are measured in the model test equipment, and good agreement is obtained for both velocity profile and jet deviation. In addition, the analysis of the bucket unsteady flow is performed using the aforementioned non-uniform jet velocity profile and the calculated flow pattern around the bucket is compared to the previous calculation using a uniform velocity profile at the inlet boundary. The difference between the two cases is discussed based on the quantitative and qualitative evaluation from the numerical analysis.