For medium-voltage (MV) high-power industrial applications including HVDC and variable-speed motor drives, multilevel converters are deemed predominant topology. One of the promising derived-topologies from neutral-point-clamped (NPC) configuration is active NPC (ANPC) inverter that offers improved characteristics. This paper proposes an improved ANPC (I-ANPC) converter controlled with an innovative logic-equation-based modulation method. The I-ANPC converter phase leg is realized by the cascaded connection of the single ANPC converter and one H-bridge cell. The H-bridge converter is formed by one flying-capacitor (FC) and four switches such as the insulated-gate bipolar transistors (IGBTs). The I-ANPC converter has considerable advantages over the classic multilevel inverters that makes it a preferable topology for MV applications. The substantial reduction in the number of cells in comparison with classic ANPC converter along with a drastic decrease in the total voltage rating and the stored energy of the capacitors are the main advantages offered by the I-ANPC multilevel converter over the FC-based inverters. This study explores the fundamental circuit of the proposed I-ANPC multilevel and its derived innovative logic-equation-based modulation technique, and provides an exhaustive comparison with FC-based classic converters. The simulation and experimental results are presented to validate the proposed I-ANPC topology and its logic-equation-based control strategy.