We present a two-layer fully connected neuromorphic system based on a thin-film transistor (TFT)-type NOR flash memory array with multiple postsynaptic (POST) neurons. Unsupervised online learning by spike-timing-dependent plasticity (STDP) on the binary MNIST handwritten datasets is implemented, and its recognition result is determined by measuring firing rate of POST neurons. Using a proposed learning scheme, we investigate the impact of the number of POST neurons in terms of recognition rate. In this neuromorphic system, lateral inhibition function and homeostatic property are exploited for competitive learning of multiple POST neurons. The simulation results demonstrate unsupervised online learning of the full black-and-white MNIST handwritten digits by STDP, which indicates the performance of pattern recognition and classification without preprocessing of input patterns.