On the onset of triple-diffusive convection in a horizontal layer of nanofluid heated from below and salted from above and below is studied both analytically and numerically. The effects of thermophoresis and Brownian diffusion parameters are also introduced through Buongiorno model in the governing equations. By using linear stability analysisbased on perturbation theory and applying normal modes analysis method, the dispersion relation accounting for the effect of various parameters is derived. The influences of solute-Rayleigh number, analogous solute-Rayleigh number, thermo-nanofluid Lewis number, modified diffusivity ratio and nanoparticle Rayleigh
number on the stability of stationary convection are presented analytically and graphically. The solute Rayleigh
number and analogous solute Rayleigh
number have stabilizing effects on the onset of stationary convection for both top-heavy and bottom-heavy arrangements. The thermo-nanofluid Lewis number and diffusivity ratio have stabilizing effects on the onset ofstationary convection while nanoparticle Rayleigh
number has destabilizing effect on the onset of stationary convection. The necessary conditions for the existence of oscillatory modes are also obtained. A very good agreement is found between the results of present paper and earlier published results.