Abstract��Hu moment invariants play a very critical role in image description. In order to construct moment invariants suitable for certain requirements briefly and verify their information redundancy effectively, a new construction method was presented by inducting the relation formula of real-complex moments. Also some concepts as moment invariants polynomial and moment invariants polynomial space were discussed so as to characterize its algebra structure. Lastly, the author listed overall practical moment invariants based on 3-order moments without informational redundancy. Compared with the typical construction approaches: algebraic theoretic construction method and triangle function construction method, this algorithm is more brief and effective, and also more suitable for discovering information redundancy. Moreover, these new moment invariants are robust and perform well in image description.