Attribute-based searchable encryption (ABSE) allows only authorized users to perform a keyword search over encrypted data in the cloud while preserving the data privacy and keyword privacy. Although ABSE provides data privacy, access control, and keyword search, it does not support data authenticity which plays a major role in the cloud environment to ensure that the data is not modified. Alongside, improving search efficiency in ABSE becomes mandatory since the cloud is attracting massive data. To address these issues, in this paper, we propose a practical verifiable multi-keyword attribute-based searchable signcryption scheme in cloud storage. The scheme uses ciphertext-policy attribute-based signcryption to achieve data privacy, access control, and data authenticity. Further, we integrate the multi-dimensional B+-tree with the Merkle tree in index construction to enhance the search efficiency and to verify the search results. The security analysis proves that our scheme satisfies security requirements such as data privacy and authenticity, index and query privacy, trapdoor unlinkability. We also prove that our scheme is secure against chosen plaintext attacks and signature forgery attacks. Finally, the performance analysis demonstrates that the proposed scheme is efficient and practical.