Fractional quantum Hall effect (FQHE) is investigated by employing normal electrons and the fundamental Hamiltonian without any quasi particle. There are various kinds of electron configurations in the Landau orbitals. Therein only one configuration has the minimum energy for the sum of the Landau energy, classical Coulomb energy and Zeeman energy at any fractional filling factor. When the strong magnetic field is applied to be upward, the Zeeman energy of down-spin is lower than that of up-spin for electrons. So, all the Landau orbitals in the lowest level are occupied by the electrons with down-spin in a strong magnetic field at 1 <ν < 2 . On the other hand, the Landau orbitals are partially occupied by up-spins. Two electrons with up-spin placed in the nearest orbitals can transfer to all the empty orbitals of up-spin at the specific filling factors ν_0 = 3 − 1 2 − 1 , (4 j + 1) (2 j + 1) and so on. When the filling factor ν deviates from ν_0 , the number of allowed transitions decreases abruptly in comparison with that at ν_0 . This mechanism creates the energy gaps at ν_0 . These energy gaps yield the fractional quantum Hall effect. We compare the present theory with the composite fermion theory in the region of 2 3 <ν < 2 .