In this paper, we proposed a high accurate and stable Legendre transform algorithm which can reduce the potential instability for very high order at a very small increase in the computational time. The error analysis of interpolative decomposition for Legendre transform is presented. By employing block partitioning of Legendre-Vandermonde matrix and butterfly algorithm, a new Legendre transform algorithm with computational complexity O(N(logN)^2/loglogN) in theory and less than O(N(logN)^4) in practical application is obtained. Numerical results are provided to demonstrate the efficiency and numerical stability of the new algorithm.