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This paper deals with the state of charge (SOC) estimation of lithium-ion battery (LIB) in electric vehicles (EVs). In order to accurately describe the dynamic behavior of the battery, a fractional 2nd-order RC model of the battery pack is established. The factional-order battery state equations are characterized by the continuous frequency distributed model. Then, in order to ensure the effective function of nonlinear function, Lipschitz condition and unilateral Lipschitz condition are proposed to solve the problem of nonlinear output equation in the process of observer design. Next, the linear matrix (LMIS) inequality based on Lyapunov’s stability theory and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> method is presented as a description of the design criteria for non-fragile observer. Compared with the existing literature that adopts observers, the proposed method takes the advantages of fractional-order systems in modeling accuracy, the robustness of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> method in restricting the unknown variables, and the non-fragile property for tolerating slow drifts on observer gain. Finally, The LiCoO<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula> LIB module is utilized to verify the effectiveness of the proposed observer method in different operation conditions. Experimental results show that the maximum estimation accuracy of the proposed non-fragile observer under three different dynamic conditions is less than 2%.