Superconductivity of nanosized Pb-island structures whose radius is 0.8 to 2.5 times their coherence length was studied under magnetic fields using low-temperature scanning tunneling microscopy and spectroscopy. Spatial profiles of superconductivity were obtained by conductance measurements at zero-bias voltage. Critical magnetic fields for vortex penetration and expulsion and for superconductivity breaking were measured for each island. The critical fields depending on the lateral size of the islands and existence of the minimum lateral size for vortex formation were observed.