β-amyloid (Aβ) protein accumulation is recognized as a key factor in Alzheimer’s disease (AD) pathogenesis. Its effects on astrocyte function appear primarily as disturbances to intracellular calcium signaling, which, in turn, affects neuronal excitability. We propose an innovative neuron-astrocyte interaction model to examine how Aβ accumulation influences astrocyte calcium oscillation and neuronal excitability, emphasizing its significance in AD pathogenesis. This comprehensive model describes not only the response of the astrocyte to presynaptic neuron stimulation but also the release of the downstream signaling glutamate and its consequential feedback on neurons. Our research concentrates on changes within two prominent pathways affected by Aβ: the creation of Aβ astrocyte membrane pores and the enhanced sensitivity of ryanodine receptors. By incorporating these adjustments into our astrocyte model, we can reproduce previous experimental findings regarding aberrant astrocyte calcium activity and neural behavior associated with Aβ from a neural computational viewpoint. Within a specified range of Aβ influence, our numerical analysis reveals that astrocyte cytoplasmic calcium rises, calcium oscillation frequency increases, and the time to the first calcium peak shortens, indicating the disrupted astrocyte calcium signaling. Simultaneously, the neuronal firing rate and cytosolic calcium concentration increase while the threshold current for initiating repetitive firing diminishes, implying heightened neuronal excitability. Given that increased neuronal excitability commonly occurs in early AD patients and correlates with cognitive decline, our findings may highlight the importance of Aβ accumulation in AD pathogenesis and provide a theoretical basis for identifying neuronal markers in the early stages of the disease.