The unstable flow phenomena in compressors, such as stall and surge, are closely related to the efficiency and the operating region. It is indispensable to capture the unstable flow structure in compressors and understand the mechanism of flow instability at low flow rates. Cooperated with the manufacturer, an industrial centrifugal compressor with a vaneless diffuser is tested by its performance test rig and our multi-phase dynamic measurement system. Many dynamic pressure transducers are circumferentially mounted on the casing surface at seven radial locations, spanning the impeller region and the diffuser inlet region. The pressure fields from the design condition to surge are measured in details. Based on the multi-phase dynamic signals, the original location of stall occurring can be determined. Meanwhile, the information of the unstable flow structure is obtained, such as the circumferential mode and the propagating speed of stall cells. To get more details of the vortex structure, an unsteady simulation of this tested compressor is carried out. The computational result is well matched with the experimental result and further illustrates how the unstable flow structure in the impeller region gradually affects the stability of the total machine at low flow rates. The dynamic mode decomposition (DMD) method is applied to get the specific flow pattern corresponding to the stall frequency. Both experimental and computational analysis show that the flow structure at a particular radial location in the impeller region has a great impact on the stall and surge. Some differences between the computational and experimental result are also discussed. Through these two main analytical methods, an insight into the unstable flow structure in an industrial compressor is gained. The result also plays a crucial role in the guidance of the compressor stabilization techniques.