Memory is vital and indispensable for organisms and brain-inspired intelligence to gain complete sensation and cognition of the environment. In this work, a memristive bionic memory circuit inspired by human memory model is proposed, which includes 1) receptor and sensory neuron (SN), 2) short-term memory (STM) module, and 3) long-term memory (LTM) module. By leveraging the in-memory computing characteristic of memristors, various functions such as sensation, learning, forgetting, recall, consolidation, reconsolidation, retrieval, and reset are realized. Besides, a multisensory mutual associative learning network is constructed with several bionic memory units to memorize and associate sensory information of different modalities bidirectionally. Except for association establishment, enhancement, and extinction, we also mimicked multisensory integration to manifest the synthetic process of information from different sensory channels. According to the simulation results in PSPICE, the proposed circuit performs high robustness, low area overhead, and low power consumption. Combining associative memory with human memory model, this work provides a possible idea for further research in associative learning networks.