Abstract: Density stratification induced by vertical temperature and salinity gradients is a typical characteristic of oceanic environments. In such density-stratified fluids, layering state are commonly observed and characterized by a stack of the convective mixing layers separated by the interfaces with high scalar gradients. This layering states can significantly influence the vertical transport and mixing of heat, salt, and density. However, the underlying mechanism which produces the layering is highly complex and not fully understood. For the fluid layer with both stably stratified temperature and salinity gradients and under the influence of background shear with uniform strength, we proposed a non-linear layering mechanism induced by finite amplitude perturbations. The initial perturbation has to be strong enough to trigger the local gravitational unstable motions, which then extract energy from the background shear flow and grow into layers. Two-dimensional direct numerical simulations confirm that this mechanism can indeed trigger the layering formation. Further analysis demonstrates that the intensity of temperature gradient directly modulates the smoothness of density interfaces, while the layering configuration of the mean density profile is predominantly controlled by the total density distribution. Notably, the instantaneous heat and salt fluxes within the flow field exhibit strong correlations with each other, as both transport processes are dominated by the spatial oscillatory motions of high-gradient interfaces. These findings reveal coupled dynamics between thermal and haline components in stratified turbulence. The current study not only describes a new mechanism of the doubly stratified fluid layer which is highly relevant to the oceanic turbulence process, but also provides valuable insights for developing accurate parameterization models of turbulent mixing in the ocean.