A surface plasmon polaritons (SPPs) interferometer array structure composed of a metal slit-groove structure was designed. Under monochromatic light illumination, the SPPs excited by the periodic grooves interfere with the direct transmitted light at the nano-slit. The phase difference between the two interfering light beams caused variations in the transmitted light intensity. Seven interferometer structures with different slit-groove distances were used to detect the refractive index of the surrounding medium by comprehensively analyzing the changes in transmitted energy. The sample was fabricated using focused ion beam milling technology to create the slit-groove structure on a metal film and was then encapsulated into a microfluidic chip. The distribution of transmitted light energy was collected under different refractive index solutions. By training and testing a backpropagation (BP) neural network model, the sensor system achieved an identification accuracy of 96.2% within a refractive index error of ±1×10^-3, demonstrating excellent generalization ability and robustness.