There are provided glass-ceramics having a high lithium ion conductivity which include in mol %: TABLE-US-00001 P.sub.2O.sub.5 38 40% TiO.sub.2 25 45% M.sub.2O.sub.3 (where M is Al or Ga) 5 15% Li.sub.2O 10 20% and contain Li.sub.1+X(Al, Ga).sub.XTi.sub.2-X(PO.sub.4).sub.3 (where 0