  A $^{59}$Co nuclear magnetic resonance (NMR) measurement was performed on the
single-crystalline ferromagnetic (FM) superconductor UCoGe under a pressure of
1.09 GPa, where the FM state is suppressed and superconductivity occurs in the
paramagnetic (PM) state, to study the superconducting (SC) state in the
PMstate. $^{59}$Co-NMR spectra became broader but hardly shifted across the SC
transition temperature. The Knight-shift change determined from fitting the
spectral peak with a Gaussian was much smaller than the spin part of the Knight
shift; this is in good agreement with the spin-triplet pairing suggested from
the large upper critical field. The spectrum broadening in the SC state cannot
be attributed to the SC diamagnetic effect but is related to the properties of
spin-triplet superconductivity. The origins of the broadening are discussed
herein.
