The background magnetic field has an important influence on the long-term closed-loop operation and the uncertainty evaluation for atomic optical clocks. The second-order Zeeman shift introduced by the backgroundmagnetic field is one of the important terms to be considered. In this paper, we firstly measure the spacing difference of the Zeeman splitting corresponding to the two transitions of ytterbium clock transition 1S0→3P0 along with the different background magnetic field. Secondly, the spacing difference of the Zeeman splitting along with the driven current of the shielding magnetic field is obtained. Finally, the driven current of the shielding magnetic field used to generate the minimum the spacing difference of the Zeeman splitting is derived in three dimensions. Based on the measurement, the second-order Zeeman shift can be obtained by tuning the polarizing magnetic field in high and low modes by self-comparison method. The result shows the coefficient of the second-order Zeeman shift is －0.0655(3)?Hz/G2 and the uncertainty due to the second-order Zeeman shift is 5.7×10－17. This work will contribute to the total uncertainty budget of our ytterbium lattice clock in the future.