Meissner diamagnetic effect is a basic criterion for identifying whether a matter is superconducting or not. However, currently one of main methods to measure magnetic property of a superconductor is ac mutual inductance technique by which ac magnetic susceptibility is measured. To investigate the relation between Meissner diamagnetic effect and the diamagnetism measured by ac susceptibility, we designed and performed an ac susceptibility experiment, that is, ac susceptibility of a superconductor as a function of temperature is measured under a constant dc magnetic field. Our experimental result shows that bulk and surface diamagnetism cannot occur in a superconductor simultaneously. This conclusion further proves that the signal of ac magnetic susceptibility gives no evidence for Meissner effect. Microscopic model and analysis on bulk and surface superconducting diamagnetism was given in the present paper.