Drawing inspiration from neurosciences, artificial neural networks (ANNs) have evolved from shallow architectures to highly complex, deep structures, yielding exceptional performance in auditory recognition tasks. However, traditional ANNs often struggle to align with brain regions due to their excessive depth and lack of biologically realistic features, like recurrent connection. To address this, a brain-like auditory network (BAN) is introduced, which incorporates four neuroanatomically mapped areas and recurrent connection, guided by a novel metric called the brain-like auditory score (BAS). BAS serves as a benchmark for evaluating the similarity between BAN and human auditory recognition pathway. We further propose that specific areas in the cerebral cortex, mainly the middle and medial superior temporal (T2/T3) areas, correspond to the designed network structure, drawing parallels with the brain's auditory perception pathway. Our findings suggest that the neuroanatomical similarity in the cortex and auditory classification abilities of the ANN are well-aligned. In addition to delivering excellent performance on a music genre classification task, the BAN demonstrates a high BAS score. In conclusion, this study presents BAN as a recurrent, brain-inspired ANN, representing the first model that mirrors the cortical pathway of auditory recognition.