The invention is concerned with an additive for a non-aqueous electrolyte of a secondary battery having a high ability dissolving a support salt and a low viscosity and comprising a phosphazene derivative represented by the following formula (I): ##STR00001## (wherein R.sup.1 is independently a halogen element or a monovalent substituent; and X is an organic group containing at least one element selected from the group consisting of carbon, silicon, nitrogen, phosphorus, oxygen and sulfur) as well as a non-aqueous electrolyte secondary battery comprising an electrolyte containing this additive and having excellent high-rate characteristics.