Reed organises arms exhibitions, including the annual Defence Systems and Equipment International Exhibition in east London, through subsidiary companies.
The trust says it spent three years trying to persuade the company to give up its arms trade interests, but was unsuccessful.
The trust's original decision to invest in the publisher was based on ethical research, but Reed's involvement in arms fairs has since expanded.
Susan Seymour, chair of the trust's investment committee, said: "The trust aims to ensure, as far as possible, that its income is compatible with the Quaker values on which it was founded. It is a measure of our significant concern that we have taken the unusual step of going public on this matter."
Reed Elsevier was unavailable for comment.