Ring signature is a well-known cryptographic primitive that allows any user who has a signing key to anonymously sign a message according to a group of users. Some years ago, Hoshino et al. propose a new kind of ring signature where anybody can transform a digital signature into an anonymous signature according to a chosen group of users; authors present a pairing-based construction that is secure under the gap Diffie-Hellman assumption in the random oracle model. However this scheme is quite inefficient for large group since the generation of the anonymous signature requires a number of pairing computations that is linear in the size of the group. In this paper, we give a more efficient anonymizable signature scheme without pairing. Our anonymization algorithm requires n exponentiations in a prime order group where n is the group size. Our proposal is secure under the discrete logarithm assumption in the random oracle model, which is a more standard assumption.