Since sea state changes engine load instantaneously, the speed governing apparatus is essential for marine engine to maintain constant speed regardless of the load. As governing apparatuses, mechanical, pneumatic, and electric governors have been employed. But, recently, according to the introduction of low speed-ling stroke engines to increase thermal efficiency, the development of governor which has better response characteristics is requisite. In this paper, to design the governor that meets above requirement, author made a performance test for the existing PID control digital governor with the aid of computer simulation, and investigated digital governor applying the optimal control algorithm, then, executed computer simulation by the same way. As the result of simulations, found that the former let engine have large overshoot and long settling time at low speed, on the other hand, the latter made engine have better response. If we design and invent a good observer for delay time element so that the optimal control theory can be applied, better governor will be expected.