The rapid advancement of Large Language Model-based AI technologies has made the ability to continuously acquire, refine, and verify knowledge a critical capability for developing more autonomous and knowledge-rich AI systems. This paper introduces Agentic Self-Knowledge Augmentation (AKA), a multi-agent reasoning framework that dynamically explores, verifies, and supplements incomplete knowledge graphs (KGs), thereby enhancing both question-answering (QA) performance and knowledge completeness. Unlike conventional Knowledge Graph Question Answering (KGQA) approaches that assume fully constructed KGs, AKA integrates internal LLM knowledge with external sources to augment missing facts in real time. The framework employs two cooperative agents, the Graph Reasoning Agent (GRA) and the Graph Augmentation Agent (GAA), along with Dynamic Augmentation Representations (DAR) and Multiple Subgraph Structures (MSG), enabling scalable and trustworthy knowledge expansion. Experimental results demonstrate that AKA achieves an 18% improvement in answer accuracy over static KGQA baselines, providing a concrete step toward building AI systems capable of autonomous learning and self-verifying knowledge augmentation.