As the demand for higher quality 3D videos continues to grow, the 3D extensions of the Efficient Video Coding (3D-HEVC) standard are gradually unable to meet the needs of users. Versatile Video Coding Standard (H. 266/VVC), as an advanced video coding standard, adopts the nested Multi-Type Tree quadtree (QTMT) partitioning structure that current fast depth map coding unit (CU) partitioning methods cannot apply. Therefore, we have designed a fast intra-frame CU partitioning algorithm for VVC 3D video depth maps. Our proposed algorithm in this article consists of two steps, including two sub-algorithms. First, by analyzing the relationship between image entropy and variance and depth map CU division, we establish a bi-criterion decision algorithm to determine whether the texture complexity of the current CU is low enough to terminate its partitioning process. Then, for CUs that have been determined by the first algorithm to need further partitioning, we use a decision tree model based on Light Gradient Boosting Machine (LGBM) to predict which direction of Rate-Distortion Optimization (RDO) calculation can be skipped, which can avoid some unnecessary RDO calculations in a certain direction. The final experiment demonstrated the effect of the proposed algorithm, which can reduce 47.65% complexity of VVC 3D video intra-coding with negligible 0.23% Bjøntegaard Delta Bitrate (BDBR) increase, superior to other advanced methods.