In this paper, we are concerned with a digital fingerprinting scheme for multi-purchase where a buyer wants to buy more than a digital content. If we apply previous schemes to multi-purchase protocol, the number of execution of registration step and decryption key should be increased in proportion to that of digital contents to be purchased in order to keep unlinkability. More worse, most of fingerprinting schemes in the literature are based on either secure multi-party computation or general zero-knowledge proofs with very high computational complexity. These high complexities complicate materialization of fingerprinting protocol more and more. In this paper, we propose a multi-purchase fingerprinting scheme with lower computational complexity. In the proposed scheme, a buyer executes just one-time registration step regardless of the number of contents to be purchased. The number of decryption key is constant and independent of the number of contents to be purchased. We can also reduce the computational costs of buyers by introducing a concept of proxy-based fingerprinting protocol.