Based on the recalibrated data of >16-MeV proton omnidirectional integral fluxes obtained from NOAA POES and EUMETSAT MetOp satellites during the period from 1978 to 2014, solar cycle phase lags, the variations of proton radiation belt, and the relationships between trapped proton fluxes and F10.7 flux, cosmic ray, or sunspot number are investigated in detail. It is found that (a) the solar cycle phase lags between energetic proton fluxes and sunspot number are within 2.5 years, dependent on solar cycle, L m , B/B 0 , and proton energy; (b) at the magnetic equator, the ratios of the maximal to minimal values of 4-month smoothed monthly >16-MeV proton fluxes during the period from 1978 to 2014 increase and then decrease with increasing L m , showing the maximal value~11.24 at L m ¼ 1.15; and (c) at a magnetic field line with L m ≤ 1.15, the ratios of the maximal values in 1987 to the minimal values in 2002 for yearly >16-MeV proton fluxes decrease with increasing B/B 0 , while at a magnetic field line with L m ≥ 1.16, they increase and then decrease with increasing B/B 0 , and the maximal ratio for all magnetic field lines can reach above 20. An exponential equation with an offset is feasible to describe the relationship between the logarithm of >16-MeV proton fluxes and F10.7 flux. It can be readily used to improve the NOAAPRO model.