As a critical component of grid security, secure and efficient grid authentication needs to be well addressed. However, the most widely accepted and applied grid authentication is based on public key infrastructure (PKI) and X.509 certificates, which make the system have low processing efficiency and poor anti-attack capability. To accommodate the challenge of grid authentication, this article aims at designing a secure and efficient method for grid authentication by employing identity-based cryptography (IBC). Motivated by a recently proposed secure and efficient identity-based encryption (IBE) scheme without random oracles, an identity-based signature (IBS) scheme is first proposed for the generation of private key during grid authentication. Based on the proposed IBS and the former IBE schemes, the structure of a novel grid authentication model is given, followed by a grid authentication protocol described in detail. According to the theoretical analysis of the model and the protocol, it can be argued that the new system has improved both the security and efficiency of the grid authentication when compared with the traditional PKI-based and some current IBC-based models.