AC losses in superconductors are essential for the design of cooling system for large scale power applications. Magnesium diboride (MgB2) superconducting wires have been investigated and manufactured over the last decade due to cheap raw materials and flexibility for coil design. In addition, multifilamentary MgB2 wires have been manufactured to reduce AC losses. In this paper, self-field AC losses of multifilamentary MgB2 wires with magnetic barrier were investigated using both experimental and numerical methods. A short straight wire sample and a coil sample were tested under various temperatures and frequencies between 16 Hz and 128 Hz. The test results show that the transportation loss is independent of the operating temperature. On basis of both theoretical and numerical study, it is found that hysteresis loss in superconductor accounts only for a small fraction of the transportation losses, ferromagnetic hysteresis loss in the magnetic barrier dominates when the transport current is low, whereas eddy current loss dominates when the transport current is close to the critical current.