Cascaded H-bridge converter has been widely used and researched in industry, since it is suitable for the operation under both normal and fault conditions. This paper proposes a novel PWM strategy based on state transition for cascaded H-Bridge inverter with unbalanced DC sources to achieve high quality line-to-line output voltages and maximize the linear modulation range. In this modulation strategy, the duration time of each switching state will be modified directly through the correction value. Ranges of correction value are derived by analyzing the modulation index limitation. Then, proper correction value is added into duration times to transform the switching states and extend modulation index to the maximum value. Meanwhile, balanced AC currents can be obtained under unbalanced DC sources condition, even under larger unbalanced coefficients. Furthermore, a three-phase power control algorithm (PCA) is introduced to achieve the balanced distribution of three-phase power. Compared with the traditional zero-sequence voltage injection method, the proposed strategy is more convenient and effective theoretically, and it can be applied to the higher-level cascaded H-bridge converter. The advantage and effectiveness of the proposed strategy are verified by simulation and experiment results.