An alumina-based adsorbent and method of making exhibiting high affinity and capacity towards fluoride ions and oxyanions of phosphorus and arsenic in a broad pH range and presence of large excess of competitive ions. Alumina based adsorbent is a mixed oxide of alumina existing in tetra-, penta-, and octahedral coordination at specific ratio, and oxides of polyvalent metals of elements titanium, zirconium, tin, cerium, lanthanum, iron, or combinations thereof. The alumina based adsorbent may be used for selective removal of fluoride ion and oxyanions of phosphorus and arsenic from drinking water, industrial streams and wastes, in medicine and food industry.