We investigate the generalized braid relation for an arbitrary multipartite d-level system and its application to quantum entanglement. By means of finite-dimensional representations of quantum plane algebra, a set of dN× dN unitary matrix representations satisfying the generalized braid relation can be constructed. Such generalized braid matrices can entangle N-partite d-level quantum states. Applying the generalized braid matrices on the standard basis of product states, one can obtain a set of maximally entangled bases. Further study shows that such entangled states can be viewed as the N-partite d-level Greenberger-Horne-Zeilinger (GHZ) states.