The binding energies of the charged excitons(negative X- and positive X+ excitons) are calculated using the finite-difference method within the quasi-one-dimensional effective potential model. The effects due to the magnetic filed and quantum confinements on the binding energy are analyzed, and the following results are obtained:(1) relative electron and hole harmonic oscillator confinement each have a strong effect on the stablity of charged excitons, the binding energy of X+ is not always larger than that of X-, e.g., due to the increase of the hole harmonic oscillator length, leading to the crossing of X+ and X- lines as recently observed experimentally;(2) the magnetic field leads to an increase of the binding energy, and the magnetic field dependence of the binding energy is related to the harmonic oscillator length.