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For maneuvering target-tracking problem, suboptimal H∞filtering is a typical approach to acquire robust target trajectory with optimized conservativeness. However, for tracking a space target that has intermittent thrust, disturbance strength is time variant in finite horizon and the level of filtering robustness should become adaptive to the variation of system uncertainties. Considering that the traditional suboptimal H2/H∞filter expresses infinite-horizon robustness, kept at constant level, in this paper, we proposed a new adaptive suboptimal H∞filter (ASO-H∞F) to establish the robustness-level adaptability. The proposed ASO-H∞F is built on a standard H∞F, embedded by an adaptive mechanism. The mechanism is derived by minimizing a unified optimality-robustness cost function (ORCF), where the weight ratio we named robustness-level index (RLI) provides a flexible level of filtering robustness. The RLI is designed as a function adaptive to real disturbance strength and tunable with an innovation sensitivity exponent (ISE) of controlling the sensitivity to disturbance. With introduction of the adaptive RLI, robustness level of the ASO-H∞F can vary with real-time disturbance strength, leading to the best balance between filtering precision and accuracy. In the ASO-H∞F, ISE is the only parameter need given for filter implementation, independent with any system uncertainty. In addition, due to the extension of suboptimal scheme, the ASO-H∞F represents a unified form of suboptimal H∞filters. A numerical example of space-maneuvering target tracking has illustrated the superior estimation performance of the ASO-H∞F to other typical H∞filters.