Coupled terms are present in the Lagrangian and the corresponding differential equations of a two-dimensional charged oscillator system are nonlinearly coupled. Firstly, the coupled terms in the Lagrangian are eliminated by transformation of coordinates; secondly, the conserved quantities in new coordinates are obtained by direct integral method, and the approximate solutions are obtained by Abdomina decomposition method. Finally, the conserved quantities and the approximate solutions can be expressed in original coordinates by using the inverse transform of the coordinates. The discussion of the approximate solutions is also given in this paper.