In recent years, an ultrafine Nb3Al wires with a diameter of less than 50 mu m 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 Nb3Al 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 Nb3Al wires under conduction cooling conditions. Single and seven-stranded Nb3Al wires with different diameters (phi 67 mu m and phi 81 mu m) 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 (phi 67 mu m) and Ta (phi 81 mu m), 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.