The spectrum and relativistic wave functions of Bc system are investigated via solving the complete Salpeter equation. Emphases are put on the study of the partial waves of each JP state. Our study shows that there are three categories of JP states. The first category contains 0− and 0+ states, which are 1S0 dominant state with a small amount of P wave and 3P0 dominant state with a small amount of S wave, respectively. The second category includes the natural parity states, such as 1−, 2+, 3−, etc. Taking the 1− state as an example, we study it in two cases. One is the 3S1 dominant state with a small amount of P and D waves, and the other is the 3D1 dominant state but contains a large amount of S and P wave components. The third category includes the unnatural parity states, such as 1+, 2−, 3+, etc. For the 1+ spectrum, the states are grouped into pairs with different radial quantum numbers. Each pair contains two 1P1−3P1 mixing states, and the corresponding mixing angles are calculated by using the relativistic wave functions.