Provided is a solid state electrolyte for a rechargeable lithium battery, comprising a lithium ion-conducting polymer matrix or binder and a lithium ion-conducting inorganic species dispersed in or chemically bonded by the polymer matrix or binder, wherein the lithium ion-conducting inorganic species is selected from a mixture of a sodium-conducting species or sodium salt and a lithium-conducting species or lithium salt selected from Li2CO3, Li2O, Li2C2O4, LiOH, LiX, ROCO2Li, HCOLi, ROLi, (ROCO2Li)2, (CH2OCO2Li)2, Li2S, LixSOy, or a combination thereof, wherein X=F, Cl, I, or Br, R=a hydrocarbon group, 0