Quadtree with nested multi-Type tree (QTMT) partition structure in Versatile Video Coding (VVC) contributes to superior encoding performance compared to the basic quad-Tree (QT) structure in High Efficiency Video Coding (HEVC). However, the improvement of performance leads to an un-Avoidable increase of computational complexity. To achieve a balance between coding efficiency and compression quality, we propose a fast intra partition algorithm based on variance and gradient to solve the rectangular partition problem in VVC. First, further splitting of smooth areas is terminated. Then, QT partition is chosen depending on the gradient features extracted by Sobel operator. Finally, one partition from five possible QTMT partitions is directly chosen by computing the variance of variance of sub-CUs. The theoretical basis of our method is that a homogeneous area tends to be predicted with a larger coding unit (CU), and sub-parts of a split CU are prone to have different textures from each other. To our knowledge, this is the first attempt to apply traditional method to accelerating the rectangular partition problem in VVC intra prediction. Experimental results show that the proposed method can save averagely 53.17% encoding time with only 1.62% BDBR increase and 0.09dB BDPSNR loss compared to anchor VTM4.0.