From the security criteria of irreversibility, parallelizability and independence, we cryptanalyzed the key expansion modules of candidate block ciphers of AES, the results revealed that there exist some weaknesses inside, which may be explored by the attacker. Hence, we designed a more secure key expansion module that the round-key can satisfy three criteria above. First, we constructed a non-degenerate 2D chaotic map (2D-πeCM) with ergodicity in phase space and sufficient large chaotic range. Then based on 2D-πeCM and polynomial multiplication over Galois field, we designed an irreversible key expansion module, which could transform the initial key of arbitrary length to desired number of independent round keys in parallel. Security and statistical results demonstrated the flexible and effectiveness of the proposed key expansion module.