We formulate second-order and fourth-order energy-preserving methods with two explicit corrections for gyrocenter systemin a strong magnetic field. We theoretically show that the error bound of the two methods are independent of the small parameter. The two explicit corrections are both manifold corrections. The first correction is confined to the manifold that the Hamiltonian at current time step should equal to the Hamiltonian at former time step and the second correction is confined to the manifold that the Hamiltonian at current time step should equal to the original Hamiltonian. Numerical experiments illustrate the impact of the ò on the phase orbit and the global error. Additionally, the numerical results show that the energy-preserving methods with the first correction show its advantage in long-term energy conservation than the energy-preserving methods without correction. The energy-preserving methods with the second correction behaves better in energy conservation than those with the first correction as the energy error of the former ones can be bounded by the machine precision over long time.