A complex oxide and an oxide-ion conductor made of the complex oxide are provided. The complex oxide has a basic composition of (Sm.sub.1-xA.sub.x)(Al.sub.1-yB.sub.y)O.sub.3, wherein "A" represents at least one element selected from the group consisting of barium, strontium and calcium, "B" represents an element selected from the group consisting of magnesium, iron and cobalt, x is a value in a range of 0.10 to 0.30, and y is a value in a range of 0 to 0.30.