From biological and artificial network perspectives, researchers have started acknowledging astrocytes as computational units mediating neural processes. Here, we propose a novel biologically inspired neuron-astrocyte network model for image recognition, one of the first attempts at implementing astrocytes in spiking neuron networks (SNNs) using a standard data set. The architecture for image recognition has three primary units: the preprocessing unit for converting the image pixels into spiking patterns, the neuron-astrocyte network forming bipartite (neural connections) and tripartite synapses (neural and astrocytic connections), and the classifier unit. In the astrocyte-mediated SNNs, an astrocyte integrates neural signals following the simplified Postnov model. It then modulates the integrate-and-fire (IF) neurons via gliotransmission, thereby strengthening the synaptic connections of the neurons within the astrocytic territory. We develop an architecture derived from a baseline SNN model for unsupervised digit classification. The spiking neuron-astrocyte networks (SNANs) display better network performance with an optimal variance-bias trade-off than SNN alone. We demonstrate that astrocytes promote faster learning, support memory formation and recognition, and provide a simplified network architecture. Our proposed SNAN can serve as a benchmark for future researchers on astrocyte implementation in artificial networks, particularly in neuromorphic systems, for its simplified design.