The conceptual determination of mixed-refrigerant (MR) for a closed Joule-Thomson cryocooler is described in this paper. The thermodynamic cycle design was mainly considered to develop a cryocooler by using a compressor of domestic air-conditioning unit. The target cooling performance of the designed cryocooler is 10 W around 70 K with less than 5 kJ/kg enthalpy rise. The systematic approach of choosing a proper refrigerant among 20 different kinds of mixture for such cryogenic temperature was introduced in detail. The main components of the cryocooler are compressor, evaporator, oil separator, after-cooler, counterflow heat exchanger, and J-T expansion device. Due to the limitation of the compressor operation range, the temperature after the compression was limited below $117^{circ}C$ (390 K) and the temperature before compression was restricted above $5^{circ}C$ (278 K). 20 atm of discharging pressure (high pressure) and less than 3 atm suction pressure (low pressure) were the design conditions. The inlet temperature of a counterflow heat exchanger in the high Pressure side was about 300 K. The proper composition of the mixed refrigerant for the designed J-T cryocooler is 15% mol of$ N_2, 30% mol of $CH_4,; 30% mol; of C^2H^ 6,; 10%; mol; of; C_3H_8; and ;15%; mol; of; i-C_4H_10$.