Group signature scheme is a method of allowing a member of a group to sign a message anonymously on behalf of the group. The group administrator is in charge of adding group members and has the ability to reveal the original signer in the event of disputes. Based on controlled quantum teleportation with three-particle entangled W states, we propose a new quantum group signature scheme with designated receiver. Security analysis proves that the proposed scheme possesses the characteristics of group signature and resists the usual attacks. Compared with previous proposed schemes, this scheme follows security definition of group signature fully and meets its basic requirements.