In a rocket combustor, purely acoustic tuning of gas-liquid scheme injector is studied numerically for acoustic absorption by adopting linear acoustic analysis. Acoustic behavior in the combustor with a single injector is investigated to assure the optimum injector length. Acoustic-absorption effect of the injector is evaluated for cold condition by the quantitative parameter of damping factor as a function of injector length in the chamber for several boundary absorption coefficients. Irrespective of boundary absorption at the chamber wall, it is assured that the optimum tuning-length of the injector corresponds to half of a full wavelength of the first longitudinal overtone mode traveling in the injector with the acoustic frequency intended for damping in the chamber. Although boundary absorption affects little the tuning length of the injector, it appreciably affects damping capacity. Acoustic absorption at the wall increases with boundary absorption coefficient, but purely acoustic-damping effect induced by the tuned injector decreases with the coefficient. As another design parameter, effects of blockage at the injector inlet on acoustic tuning are investigated. It is found that the optimum injector length is shifted depending on the blockage ratio. Suitable combination of injector length and blockage should be made for maximum damping.