New geopolymer concrete with high mechanical strength - 58.9 MPa after 28 days of curing - was experimentally made under environmental friendly and economic conditions. The high-strength-geopolymer is baed on coal fly ash and building concrete waste as geopolymer materials suitable for completely substituting the cement in concrete structure. The alumino-silicate geopolymer materials with binder role were activated in liquid alkaline medium (sodium silicate and sodium hydroxide) for facilitating the polymerization reaction that turns the alumino-silicate wastes into geopolymer concrete. The use for the first time in this experiment of recycled building concrete waste from demolition is the work originality.