In this letter, we improve NF'07 (Nakanishi and Funabiki) VLR group signature scheme such that it satisfies exculpability and has lower computation costs. In the proposed scheme, a group member generates his own private key together with the group manager in order to realize exculpability while the signature size is not made longer. Also, a new revocation check method is proposed at the step of verifying, and the computation costs of verifying are independent of the number of the revoked members, while they are linear with the number of the revoked members in the original scheme. Thus, the proposed scheme is more efficient than the original scheme and can be applicable to mobile environments such as IEEE 802.1x.