Compared with High Efficiency Video Coding (HEVC), Versatile Video Coding (VVC) has significantly improved compression efficiency. However, its encoding complexity has also increased substantially. To reduce the encoding complexity of VVC, this paper designs a three-level cascaded decision algorithm based on Linear Discriminant Analysis (LDA) for quickly selecting the partition mode of 32 \(\times \) 32 coding unit (CU). The algorithm includes two modes: (1) full cascaded decision mode, which directly predicts the CU partition mode through the three-level cascaded structure; (2) partial cascaded decision + (Rate-Distortion Optimization) RDO search mode, which only performs the third-level decision and conducts RDO search on three candidates: no partition, quadtree (QT) partition, and the partition mode predicted by the third-level decision. Experimental results show that, in All Intra mode, compared with the VVC reference software VTM-23.0, at the same video quality, the proposed full cascaded decision mode saves an average of 65.4% of the encoding time and increases Bjøntegaard Delta bit rate (BDBR) by an average of 5.19%; the partial cascaded decision + RDO search mode saves an average of 33.44% of the encoding time and increases BDBR by an average of 1.29%. The proposed method uses very few parameters and provides a hardware-friendly solution for VVC encoding. We also constructed a dedicated dataset for model training and testing, and provided complete availability details in this paper.