To address the pressure maintenance problem for the insulation space of liquefied natural gas (LNG) tanks, a H_∞ optimized scheme is proposed based on the mirror-mapping technique. Firstly, the nonlinear model of the pressure maintenance system is linearized around its equilibrium, so as to obtain a kind of integral unstable time-delay model. Using the mirror-mapping technique, the unstable poles of the linear model are mapped onto the left-half complex plane, and the corresponding stable mirror-mapping model is derived. Then, the controller is developed based on the H_∞ minimum sensitivity optimization, and the robust performance for the unstable plant and the mirror-mapping one is equivalent. In addition, the proposed control law can be expressed as a PID control in series with a second order filter, and only one ``stability degree'' related parameter should be tuned to guarantee the closed-loop performance. The graphical stability criterion is adopted to determine the exact stable region for the related parameter. Finally, the simulation results verify the effectiveness and superiority of the proposed algorithm.