Recently, the researches of quantum group signature (QGS) have attracted a lot of attentions and some typical protocols have been designed for e-payment system, e-government, e-business, etc. In this paper, we analyze the security of the quantum group signature with the example of two novel protocols. It can be seen that both of them cannot be implemented securely since the arbitrator cannot solve the disputes fairly. In order to show that, some possible attack strategies, which can be used by the malicious participants, are proposed. Moreover, the further discussions of QGS are presented finally, including some insecurity factors and improved ideas.