The present invention relates to an electrolyte for producing a novel Fe—Ni alloy having an Ni content in a range of 33 to 42 wt %, specifically a nanocrystalline invar alloy having a grain size of 5 to 15 nm, by electroplating, and preparation conditions thereof. The electrolyte comprises, on the basis of 1 L of water, 32 to 53 g of ferrous sulfate or ferrous chloride, a mixture thereof; 97 g of nickel sulfate, nickel chloride, nickel sulfamate or a mixture thereof; 20 to 30 g of boric acid; 1 to 3 g of sodium saccharin; 0.1 to 0.3 g of sodium lauryl sulfate; and 20 to 40 g of sodium chloride. The Fe—Ni alloy sheet of the present invention exhibits excellent mechanical property compared to the conventional Fe—Ni alloy and a new property, i.e., a negative coefficient of thermal expansion at a given temperature range.