Renewable energy based distributed generators are key components in islanded microgrids. However, their power intermittency and uncertainty may impair power quality and cause system operating constraint violations. It is imperative to evaluate and maximize the hosting capacity of an islanded mi-crogrid for renewable generation. Besides, conventional optimi-zation methods focus on improving the solution robustness on constraints under uncertainties but ignoring that on the optimi-zation objective. To address these unsolved issues, a sensitivity region (SR) based optimization method for maximizing renewa-ble generation hosting capacity of an islanded microgrid is pro-posed. This paper firstly proposes an optimization model consid-ering microgrid frequency variation and microturbine droop control functionality. Secondly, SR and feasibility-SR are adopt-ed to quantify solution robustness against uncertainties of renew-able generation and load. It is expected to enlarge these two re-gions to cover all the possible uncertainty realizations, thus providing robust solutions. Last, this paper develops an SR based optimization method with a new solution algorithm. Through comprehensive numerical simulations, the proposed SR based hosting capacity maximization method is verified with high solu-tion robustness on both objective and operating constraints.