We report high-resolution scanning tunneling microscopy (STM) study of nano-sized Pb islands grown on SrTiO3,where three distinct types of gaps with different energy scales are revealed.At low temperature,we find that the superconducting gap (△s) in nano-sized Pb islands is significantly enhanced from the one in bulk Pb,while there is no essential change in superconducting transition temperature Tc,giving rise to a larger BCS ratio 2△s/kBTc ～ 8.31 and implying stronger electron-phonon coupling.The stronger coupling can originate from the interface electron-phonon interactions between Pb islands and SrTiO3.As the superconducting gap is totally suppressed under applied magnetic field,the Coulomb gap with apparent V-shape emerges.Moreover,the size of Coulomb gap (△C) depends on the lateral size of Pb islands (R) with △C ～ 1/R0.35,indicating that quantum size effect can significantly influence electronic correlations.Our experimental results shah shed important light on the interplay among superconductivity,quantum size effect and correlations in nano-sized strong-coupling superconductors.