To study how the geometry of the plenum chamber in the bleed system of an axial compressor influences the losses therein and to establish a theoretical loss model for this system, a 1.5-stage axial compressor with a bleed system is studied numerically by means of computational fluid dynamics (CFD). The results show that losses in the bleed system occur mainly in the axisymmetric bleed slot and plenum chamber, accounting for ca. 85% of the total loss. For a bleed system with a vertical axisymmetric slot, the loss is more sensitive to the radial height than to the axial width of the plenum chamber. A loss model for each part of the bleed system is established via theoretical analysis, and then, a model of the overall bleed system is established by combining these submodels. The predictions of the theoretical loss model agree well with the CFD results: the maximum prediction error for the coefficient of the stagnation pressure loss in the bleed system is −1.38%, and the average prediction error is −0.8%. This loss model can be used when designing the geometry of a bleed system.