We report the observation of layer-breathing mode (LBM) vibrations in few-layer graphene (FLG) samples of thickness from two to six layers, exhibiting both Bernal (AB) and rhombohedral (ABC) stacking order. The LBM vibrations are identified using a Raman combination band lying around 1720 cm(-1). From double resonance theory, we assign the feature as the LO+ZO' combination mode of the out-of-plane LBM (ZO') and the in-plane longitudinal optical mode (LO). The LOZO' Raman band is found to exhibit multiple peaks with a unique line shape for each layer thickness and stacking order. These complex line shapes of the LOZO'-mode arise both from the material-dependent selection of different phonons in the double-resonance Raman process and from the detailed structure of the different branches of LBM in FLG.