AC losses in a monofilamentary MgB 2 round wire with niobium and copper metal sheaths and carrying alternating transport currents are evaluated at several temperatures and frequencies. First, the transport current losses are observed electrically using a lock-in amplifier. Experimental results show that the AC losses decrease with an increase in the temperature if the amplitude of the transport current normalized by the corresponding critical current is maintained constant. On the other hand, the AC losses increase slightly with the frequency. Next, the AC losses are calculated numerically by a finite difference method. The numerical results for the superconductor filament show a good agreement with the results of the conventional theoretical expression formulated using the Bean model over a wide range of current amplitudes. It is also found that the AC losses in the niobium sheath are negligible whereas those in the copper sheath are comparable with those in the superconductor. On the basis of the numerical calculations, an expression is analytically derived for estimating the eddy current loss occurring in a metal sheath. The derived expression well reproduces the AC loss properties of both the copper and niobium sheaths.