In this paper, we propose a formal definition for Linked-Data based verifiable credential to enable secure selective disclosure among one or multiple verifiable creden-tials a user has. Previous schemes considered using a single verifiable credential and could not hide the user's identifying information when performing selective disclosure. We pro-pose the first Linked-Data based verifiable credentials that can perform selective disclosure free from the restrictions the previous scheme had, and prove its property. We also discuss a novel use of combining multiple certificates issued by independent issuers to still allow users to perform selective disclosure on the set of credentials. Our scheme has been implemented as an open source Web-based application that generates a verifiable presentation for a given selection of attributes. The performance evaluation is also provided in the paper.