An alumina-based adsorbent and method of making exhibiting high affinity and capacity towards cations and oxyanions 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 oxyanions of fluoride, phosphorus, arsenic, chromium, and/or selenium, and/or cations of lead, mercury, cadmium, copper, and/or zinc, from drinking water, industrial streams and wastes, in medicine and food industry.