Blind signature is a special type of digital signature, the signer cannot see the specific content signed. However, blindness may cause users to abuse their rights. Partial blind signature allows the signer to embed pre-negotiated public information in the blind signature without losing blindness, which can prevent users from abusing their rights. Islam et al. presented an identity-based partial blind signature scheme and claimed that it is provable secure. However, in this paper we proved that the scheme is vulnerable against the tampering attacks with public information. We then proposed a new identity-based partial blind signature scheme, showed the security proofs under the assumption that the elliptic curve discrete logarithm problem (ECDLP) is difficult. The new scheme does not use pairing operations and enjoys less computation cost.