It is shown that the cosmological constant problem in brane-world is different from the same problem in general relativity, essentially because the gauge fields fields contributing to the vacuum energy are confined to the brane-world, but the cosmological term propagates in the bulk. The brane-wrld equations of motion include a second order, conserved symmetric tensor field in four dimensions defined by the extrinsic curvature, which adjusts the vacuum energy. In the application to the FRW brane-world universe embedded in a five-dimensional deSitter bulk, that tensor modifies Friedman's equation with a remarkable agreement with the current gold set of cosmological data.