In recent years, an ultrafine Nb<sub>3</sub>Al wires with a diameter of less than 50 μm has been developed by a research group at the National Institute for Materials Science (NIMS) in Japan. Therefore, we are planning to use the developed high performance Nb<sub>3</sub>Al wires for superconducting applications operated by cryocooler. In order to design the superconducting applications cooled by cryocooler, it is necessary to measure the temperature and magnetic field dependence of the critical current of Nb<sub>3</sub>Al wires under conduction cooling conditions. Single and seven-stranded Nb<sub>3</sub>Al wires with different diameters (ϕ67 μm and ϕ81 μm) fabricated by the Jelly-rolled method were prepared. The barrier material of the two samples is the same Nb, but the core materials are Nb (ϕ67 μm) and Ta (ϕ81 μm), respectively. The Cu/nonCu ratio of the two samples is 1. In this study, the critical currents of sample wires were measured by a four-probe method with current sweep and constant current, and they were compared to define a reasonable critical current value under conduction cooling. Under conduction cooling, it was confirmed that the critical current measurement by the constant current method was more accurate than the current sweep method.