Upward-heating multiple-effect diffusion solar still (UHMEDS) coupled with a parabolic dish concentrator (PDC) was proposed and analyzed theoretically. UHMEDS has cover glass, several partitions and preheating cover, and wicks are placed on the upper surfaces of partitions and preheating cover. Saline water preheated on the preheating cover flows down the partitions by gravitational force. The lowermost partition of UHMEDS was heated by solar energy collected by PDC. The basic behavior of UHMEDS at Fukuoka, Japan was analyzed theoretically by modeling heat and mass transfer in the still. The theoretical results show that PDC can collect the sunrays to the lowermost partition of UHMEDS effectively, and the overall daily productivity of the still was predicted to be about 18.5, 24.5 and 10.4 kg/m2day on spring equinox, summer and winter solstice days, respectively, which values are almost equivalent to those of other types of multiple-effect diffusion solar still.