A scheme was proposed to construct bilinear and quadratic Hamiltonians for frequency up- and down-conversions in cavity quantum electrodynamics (QED). Generally, in nonlinear optics, the interaction that the energe swaps between different optic modes without atomic transition is named frequency conversion. The proposed scheme was based on the interactions of a single four-level atom simultaneously with two classical driving fields and a two-mode cavity field, which is in the domain of four-wave mixing . By initially preparing the atom in a suitable state, each pump light was resonant with its transition, and two quantum modes were large tune to the other two transition, respectively, In the strong laser regime, the atomic degrees of freedom could be decoupled from the cavity degrees of freedom and the frequency conversion could be realized for the cavity modes. Due to the different initial states and interactions between optic fields and atom, frequency up- and down-conversions arose, respectively. After the preparation of squeezed operation respect to Frequency down-conversion, a discussion on the feasibility of experiment was given and the theoretical value was obtained. The advantage of this proposal is to realize the transition using two cascade photons, which is dipole-forbidden in a cascade structure atom, with high efficiency. The proposal will be useful for optical quantum control and fundamental tests of quantum theory.