In the rapid development of high-performance parallel computing technology today, the demand of science and engineering numerical calculation is higher and higher. In the numerical calculations, the final solution is converted into the calculation of large-scale system of linear equations. This article focuses on parallel algorithm of tridiagonal equations. Firstly, introduce the current solving tridiagonal linear equations on parallel algorithms: direct solution and the iterative solution. Direct solution, the algorithm is rich, the program is easy to implement, but the amount of calculation is too large, and most of the algorithms for the requirement of the coefficient matrix is relatively high. Iterative solution is more suitable for nonzero elements, especially the iteration solution combination with Krylov subspace. Then, by using the orthogonal projection method, greedy method and partition strategy method, a new parallel iterative procedure is used to solve arbitrary tridiagonal equations. Finally, give a new proof of convergence of the algorithm.