Quantum key distribution (QKD) and quantum key agreement (QKA) are two main branches of key establishment in quantum cryptography. However, the research of QKA falls far behind that of QKD, especially in practicability. The main reason is that QKA needs to resist not only the outside eavesdropping but also the participant cheating. Resisting dishonest participant is more difficult than resisting outside eavesdropping, especially when the apparatuses are imperfect. Actually, existing QKA protocols cannot tolerate the channel loss and have to rely on stable quantum storage. To solve this problem, we give a new quantum multi-party key agreement protocol based on the error-correcting code. Our protocol is loss tolerant, and the participants can measure the received qubits immediately in one of two conjugate bases, without storage, so our protocol can eliminate the requirement of quantum storage. Besides, our protocol is more fair because it can partially discriminate dishonest participants' cheating from outside eavesdropping (previously, these two attacks are generally checked simultaneously via decoy states but cannot be discriminated), as a result, dishonest participants generally will not cheat at the cost of losing good reputation.