Matrix transpose is one of the common matrix operations, which is widely employed in various fields such as signal processing, scientific computing, and deep learning. With the popularization of Phytium heterogeneous multi-core DSPs(digital signal processors) developed by National University of Defense Technology, there is a strong demand for high-performance matrix transpose implementations for Phytium multi-core DSPs. Based on the architecture of multi-core DSPs and the characteristic of matrix transpose operations, a parallel matrix transpose algorithm (called ftmMT) for matrices with different element bit widths (8 B, 4 B, and 2 B) was proposed. In ftmMT, the main optimizations include vectorization based on vector Load/Store functions, core-level parallelization based on matrix blocking, and overlapping between vectorization and memory access through implicit ping-pong methods. The experimental results show that ftmMT can significantly improve the performance of matrix transpose operations, and achieve a speedup of up to 8.99 times in comparison with the open-source transpose library HPTT running on CPU.