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We present an experimentally feasible one-step discrimination scheme on Bell bases with trapped ions, and then generalize it to the case of N-ion Greenberger-Hoe-Zeilinger (GHZ) bases. In the scheme, all the orthogonal and complete N-ion GHZ inteal states can be exactly discriminated only by one step, and thus it takes very short time. Moreover, the scheme is insensitive to thermal motion and dose not require the individual addressing of the ions. The Bell-state and GHZ-state one-step discrimination scheme can be widely used in quantum information processing based on ion-trap set-up.