Divide and conquer algorithm is widely used for tridiagonal matrix eigenproblems while computing efficiency and storage limitation are always bottlenecks for large scale problems. In this study, the proposed eigenproblem algorithm based on hybrid parallel paradigm with MPI/Cilk optimizes the divide and conquer algorithm both at data and task levels. The introduced task-based parallelization mechanism inside computing nodes solves the problem in data dependence and thread starvation by directed acyclic graph model. By coarse-grained partition of tasks the overhead of data communication among MPI nodes is also optimized, which helps to improve load balance. The numerical test is carried out and the result is compared with the pure MPI and MPI/openMP parallel algorithm, which shows the performance and efficiency of the algorithm.