This study investigates the time-dependent double-diffusive convection of NaCl-H2O concerning the stably stratified salt fluid layer with lateral heating in an inclined cavity. The N-S equations are solved via a finite difference method with Ra = 1 x 10(7) and Ra-s = 5 x 10(7). The plots of stream function, isotherms and isosolutal lines at inclined angles from gamma = 75 degrees to -75 degrees during a long period of time are presented and systematically discussed. At early time, there are two types of instability onset. At gamma < 75 degrees, the cells rotate strikingly in one sense of rotation, but weakly in the other, while at gamma greater than or equal to 75 degrees the comparable vortexes rotating in a different sense are generated. The onset of instability is nonsymmetric, being faster at negative angles than at positive ones. The multi-layered structure is formed with a sharp solutal difference and a wavy distribution of temperature at all inclined angles. The distribution of local Nusselt number is periodic due to the layered structure. The average Nusselt number with respect to time reveals more detailed information about the heat transfer behavior of layer forming, propagating and merging. The prediction of final layer thickness and flow field agrees well with the experiments and flow visualization.