The use of the bi-conductive surface provides a promising prospect for the enhancement of the boiling phase change heat transfer. In this study, a theoretical model of two-phase flow and boiling heat transfer on bi-conductive surfaces is developed. With the consideration of thermal conductivity contrast and conjugate heat transfer, the boiling behavior is numerically investigated based on a modified lattice Boltzmann method. The bubble dynamics during the boiling process on the bi-conductive surface are reproduced and the effect of the structural size of these insets on the boiling performance is explored. The results indicate that boiling performance is enhanced on the bi-conductive surface when compared to homogeneous ones. In-plane temperature variation on the surface contributes to the pinning effect on bubble contact lines, and thus promotes boiling heat transfer. Boiling enhancement gets optimized once the embedding pitch space equal to the capillary length of the boiling fluid. Increasing the width of the insets also improves the boiling heat transfer coefficient on the bi-conductive surface under low superheat conditions, but also leads to the advance of CHF. However, changing the depth of the insets shows almost no effect on the boiling heat transfer performance.