The proposed work presents the design and application of many-objective Jaya (MaOJaya) algorithm to optimize many-objective benchmark optimization problems. The basic Jaya algorithm is modified by introducing non-dominated sorting and tournament selection scheme of NSGA-II. The reference point mechanism is introduced to traverse algorithm towards the best solutions. The basic Jaya algorithm is modified while preserving its essential properties. The Tchebycheff-a decomposition based approach is used to simplify the complex MaOPs. The proposed MaOJaya algorithm is tested on DTLZ benchmark functions with objectives ranging from three to ten to measure its applicability and effectiveness to solve many-objective optimization problems. The IGD and Hypervolume performance metrics are used to evaluate the performance of proposed MaOJaya algorithm. The obtained IGD and Hypervolume values compared with the best known results and it is observed that, the proposed MaOJaya algorithm gives competitive or better results than known best results.