This paper presents a formal framework for semi-automated verification of security proofs of quantum cryptographic protocols. We simplify the syntax and operational semantics of quantum process calculus qCCS so that verification of weak bisimilarity of configurations becomes easier. In addition, we generalize qCCS to handle security parameters and quantum states symbolically. We then prove the soundness of the proposed framework. A software tool, named the verifier, is implemented and applied to the verification of Shor and Preskill's unconditional security proof of BB84. As a result, we succeed in verifying the main part in Shor and Preskill's unconditional security proof of BB84 against an unlimited adversary's attack semi-automatically, i.e., it is automatic except for giving user-defined equations.