75As-nuclear magnetic resonance (NMR) on an iron-based superconductor LaFeAsO1-xFx (x=0.14) was performed under a pressure of 3GPa. Enhancement of superconducting transition temperature Tc was confirmed from the relaxation rate 1/T1; Tc goes up to 40K by applying pressure up to 3GPa. 1/T1T, which is temperature independent just above Tc and gives a measure of the density of states (DOS) at the Fermi energy, enhances by applying pressure. These facts suggest that the increase of the DOS leads to the enhancement of Tc. On the other hand, anomalous behavior of 1/T1T observed at high temperatures is suppressed by applying pressure.