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We propose a provably secure blind ID-based strong designated verifier signature (BIDSDVS) scheme in this paper. We first define the BIDSDVS scheme model with the relevant security notions. Then a new concrete provably secure IDSDVS scheme is presented with the random oracle model. Based on our IDSDVS scheme, we give the BIDSDVS scheme, and provide the proofs of the blindness and the parallel one-more unforgeability (plm-uf) which is reduced to Schnorrs ROS Problem in the random oracle model plus the generic group and pairing model (ROM+GGPM).