The reaction rate of the 3He−α radiation capture process has been calculated in astrophysical energies using the pionless Effective Field Theory (EFT) and applying the Faddeev equation approach up to Next-to Leading Order (NLO) while taking Coulomb interaction into account. The findings for the E1 and E2 transitions to the 7Be ground state have been normalized using NACRE 1999 experimental data and compared to the certain theoretical and experimental data.