A 1 MVA single-phase high temperature superconducting (HTS) transformer with BSCCO-2223 wire was designed in this paper. The rated voltages of each sides of the transformer are 22.9 kV and 6.6 kV respectively. Double pancake HTS windings arranged reciprocally will be used for the transformer windings, because of the advantages of insulation and distribution of surge voltage in case of a large power and high voltage transformer. Single HTS wire was used for the primary windings and four parallel wires were used for the secondary windings of the transformer with transposition. A core of the transformer was designed as a shell type core separated with the windings by a cryostat made of GFRP with a room temperature bore. The operating temperature of the HTS windings will be about 65K with sub-cooled liquid nitrogen. A cryogenic cooling system using a GM-cryocooler for this HTS transformer by natural convection of liquid nitrogen was designed. This type of cooling system can be a good option for compactness, efficiency, and reliability of the HTS transformer.