As state of charge is one important variable to monitor the later battery management system, and as traditional Kalman filter can be used to estimate the state of charge for Lithium-ion battery on basis of probability distribution on external noise. To relax this strict assumption on external noise, set membership strategy is proposed to achieve our goal in case of unknown but bounded noise. External noise with unknown but bounded is more realistic than white noise. After equivalent circuit model is used to describe the Lithium-ion battery charging and discharging properties, one state space equation is constructed to regard state of charge as its state variable. Based on state space model about state of charge, two kinds of set membership strategies are put forth to achieve the state estimation, which corresponds to state of charge estimation. Due to external noise is bounded, i.e. external noise is in a set, we construct interval and ellipsoid estimation for state estimation respectively in case of external noise is assumed in an interval or ellipsoid. Then midpoint of interval or center of the ellipsoid are chosen as the final value for state of charge estimation. Finally, one simulation example confirms our theoretical results.