Group signature scheme provides a way to sign messages without revealing identities of the authentic signers. To achieve such functionality and to avoid the abuse of its power, anonymity and traceability are two essential properties for group signature scheme. In traditional group signature schemes, however, these two security properties are based on the perfectly-secure storage of secret information. Unfortunately, defective implementation of a cryptosystem always exists, and therefore unexpected information leakage is inevitable. In reality, side-channel attacks allow an adversary breaks the security of the whole system by eavesdropping a portion of secret information. To tackle this issue, in our work we present the security models of leakage-resilient group signature in bounded leakage setting and furthermore, propose three new black-box constructions of leakage-resilient group signature based on the proposed security models.