The Joint Video Exploration Team (JVET) recently launched the standardization of next-generation video coding named Versatile Video Coding (VVC) in which the Adaptive Multiple Transforms (AMT) is adopted as the primary residual coding transform solution. AMT introduces multiple transforms selected from the DST/DCT families and achieves noticeable coding gains. However, the set of transforms are calculated using direct matrix multiplication which induces higher run-time complexity and limits the application for practical video codec. In this paper, a fast DST-VII/DCT-VIII algorithm based on partial butterfly with dual implementation support is proposed, which aims at achieving reduced operation counts and run-time cost meanwhile yield almost the same coding performance. The proposed method has been implemented on top of the VTM-1.1 and experiments have been conducted using Common Test Conditions (CTC) to validate the efficacy. The experimental results show that the proposed methods, in the state-of-the-art codec, can provide an average of 7%, 5% and 8% overall decoding time savings under All Intra (AI), Random Access (RA) and Low Delay B (LDB) configuration, respectively yet still maintains coding performance.