As an important part of quantum cryptography, quantum blind signature has attracted more and more attention in recent years. Semi-quantum protocol provides a feasible method for the practical application of quantum blind signature. In this paper, a semi-quantum blind signature protocol against collective noise is proposed by combining the semi-quantum and logical qubits resisting collective noise. In the protocol, only the signer Charlie has the complete quantum capability, which makes the demand for quantum resources of the protocol drop drastically. Through security analysis, the protocol can resist internal attack, entanglement-measurement attack and intercept-resend attack. The protocol implements reusability of keys and the scheme can be extended to quantum signature networks to realize cross-center quantum signature.