75 As-nuclear magnetic resonance (NMR) on an iron (Fe)-based superconductor LaFeAsO 1- x F x ( x =0.14) was performed under a pressure of 3 GPa. Enhancement of the superconducting transition temperature ( T c ) was confirmed from the relaxation rate (1/ T 1 ); T c goes up to 40 K by applying pressure up to 3 GPa. 1/ T 1 T , which is temperature independent just above T c and gives a measure of the density of states (DOS) at the Fermi energy, enhances by applying pressure. These facts suggest that an increase of the DOS leads to the enhancement of T c . On the other hand, anomalous behavior of 1/ T 1 T observed at high temperatures is suppressed by applying pressure.