A novel hybrid Freeman/eigenvalue decomposition with general scattering models was proposed for polarimetric synthetic aperture radar (PolSAR) data. A unit matrix represents the volume scattering model, and eigenvectors corresponding to the two larger eigenvalues of the coherency matrix are used as the surface scattering model and double-bounce scattering model for non-reflection symmetry condition. There are three advantages in the proposed hybrid decomposition. Firstly, the surface and double-bounce scattering models are free from the reflection symmetry constraint which is more general and realistic for common media. Secondly, since the scattering powers of the proposed method are solved as linear combinations of the eigenvalues derived from the coherency matrix, they are all roll-invariant parameters. Thirdly, negative powers of surface scattering and double-bounce scattering are avoided with non-rotation of the coherency matrix. Fully PolSAR data on San Francisco are used in the experiments to prove the efficacy of the proposed hybrid decomposition.