Bundles of carbon fibers were successfully coated with alumina by atomic layer deposition via sequential exposures to trimethyl-aluminum and water at 77 degrees C. Fibers were not damaged by this procedure. Scanning electron microscopy (SEM) images revealed that individual filaments were coated separately with a smooth layer; no bridging of fibers was observed. Transmission electron microscopy (TEM) and SEM images indicate that the coating was conformal and adhered well to the fiber surface. The average deposition rate was 0.25 +/- 0.02 nm/cycle, calculated from SEM images obtained at various positions of the fibers and of fibers coated with various numbers of cycles. In addition to image analysis, the coating thickness was as well estimated from the elemental composition of selected parts of a fiber bundle that was coated by 450 cycles. Along the fiber axis, the weight fraction of aluminum of the coated fibers varied from 5.3 to 6.5 wt% and perpendicular to the bundle axis it varied from 4.8 to 7.4 wt%. This translates into a variation of the estimated coating thickness along the fiber from 166 to 126 nm and perpendicular to it from 114 to 183 nm. One can estimate independently an average coating thickness from the analysis of SEM images of this specific bundle of 126 nm. The alumina coating improved oxidation resistance of the carbon fiber significantly. The oxidation onset temperature was 600 degrees C for fibers coated with a 30-nm-thick layer of alumina and increased gradually with increasing coating thickness up to 660 degrees C at a thickness of 120 nm. On the other hand, uncoated fibers started to oxidize already at 300 degrees C.