We present a new cognitive architecture that combines two neurobiologically-plausible computational elements: (1) a variant of predictive processing known as neural generative coding and (2) hyperdimensional / vector-symbolic models of human memory. We draw inspiration from well-known cognitive architectures such as ACT-R, Soar, Leabra, and Spaun/Nengo. Our cognitive architecture, the COGnitive Neural GENerative system (CogNGen), is in broad agreement with these architectures, but provides a level of detail between ACT-R’s high-level, symbolic description of human cognition and Spaun’s low-level neurobiological description. CogNGen creates the groundwork for developing agents that learn from diverse tasks and model human performance at larger scales than what is possible with existent cognitive architectures. We test CogNGen on a set of maze-learning tasks, including mazes that test short-term memory and planning, and find that the synergy between its predictive processing and vector-symbolic components allow it to master the maze tasks.