The single-electron tunneling behavior of crystalline palladium nanoparticles with narrowly distributed core sizes ranging from 1.6 to 4nm is studied by scanning tunneling microscopy/spectroscopy. The current-voltage (I-V) characteristics of Pd nanoparticles exhibit size-dependent fine features, which are assigned to the discreteness of energy states of the ultrasmall Pd particles. It is found that the peak widths, as well as the intrapeak spacings in differential conductance dI/dV spectra increase with the decrease of the size of Pd nanoparticles. Our analysis shows that the dwell time of the weak tunnel junction may not be a major contribution to the peak widths due to the large resistance of the tunnel junction of about 107π. The possible effect of residual charge is also excluded. An explanation of the size-dependent behaviors of the peak width and the intrapeak spacing is attributed to the clustered electronic structures around the Fermi level due to certain size-dependent dynamic effects.