Numerical study has been conducted to study the fluid convection inside sessile and pendant evaporating droplets of aqueous NaCl solution placed on a superhydrophobic surface. Evaporation from the droplet surface leads to increase in the solute concentration at the evaporating liquid–air interface generating concentration gradient inside the droplet. Concentration gradient inside the droplet induces Rayleigh convection. Fluid with higher concentration in the liquid–air interface region moves downward along the interface and lighter fluid rises upward along the central region of the droplet like a plume. The average concentration, evaporation rate and the maximum velocity inside the sessile droplet on a superhydrophobic surface is higher than that on a hydrophobic surface. Both sessile and pendant droplet configurations have been investigated. Fluid near the interface moves towards the substrate in case of sessile droplet, where as the fluid moves away from the substrate along the interface for the pendant droplet configuration. Two counter rotating recirculation bubbles are observed in both sessile and pendant droplets. The magnitude of maximum convection velocity and circulation strength of the recirculation bubbles for pendant droplet is smaller than that of sessile droplet at the same evaporation conditions. This may be attributed to the stratification of higher density fluid for the pendant droplet configuration which suppresses the Rayleigh convection. The effect of initial solute concentration on the strength of convection is stronger for sessile droplet configuration compared to that of pendant droplet. The present study establishes strong influence of superhydrophobicity and orientation on the internal convection inside a droplet of aqueous solution.