Disclosed is an improved solid electrolyte made of an interpenetrating network type solid polymer comprised of two compatible phases: a crosslinked polymer for mechanical strength and chemical stability, and an ionic conducting phase. The highly branched siloxane polymer of the present invention has one or more poly(ethylene oxide) ("PEO") groups as a side chain. The PEO group is directly grafted to silicon atoms in the siloxane polymer. This kind of branched type siloxane polymer is stably anchored in the network structure and provides continuous conducting paths in all directions throughout the IPN solid polymer electrolyte. Also disclosed is a method of making an electrochemical cell incorporating the electrolyte. A cell made accordingly has an extremely high cycle life and electrochemical stability.