Secret sharing is a useful method for secure distributed data storage. Such a distributed data storage can avoid the information leakage under an attack to a limited number of distributed servers. While such distributed servers send their shares to an end user according to the request, there is a risk that malicious distributed servers send incorrect shares. To detect or identify such malicious servers, we need verifiable secure distributed data storage, which can be constructed from verifiable secret sharing. However, many of previous protocols for verifiable secret sharing are constructed in a specific form. This paper proposes an adaptive construction of verifiable secret sharing, which uses an existing secret sharing protocol as a subprotocol. Also, our method can be applied to any existing secret sharing protocol. This type construction realizes an economical construction.