Anonymous credentials are protocols in which users obtain certificates from organizations and subsequently demonstrate their possession in such a way that transactions carried out by the same user cannot be linked. We present an anonymous credential scheme with non-interactive proofs of credential possession where credentials are associated with a number of attributes. Following recent results of Camenisch and Groß (CCS 2008), the proof simultaneously convinces the verifier that certified attributes satisfy a certain predicate. Our construction relies on a new kind of P-signature, termed block-wise P-signature , that allows a user to obtain a signature on a committed vector of messages and makes it possible to generate a short witness that serves as a proof that the signed vector satisfies the predicate. A non-interactive anonymous credential is obtained by combining our block-wise P-signature scheme with the Groth-Sahai proof system. It allows efficiently proving possession of a credential while simultaneously demonstrating that underlying attributes satisfy a predicate corresponding to the evaluation of inner products (and therefore disjunctions or polynomial evaluations). The security of our scheme is proved in the standard model under non-interactive assumptions.