Summary: In this paper, the nonnegative \(Q\)-matrix completion problem is studied. A real \(n\times n\) matrix is a \(Q\)-matrix if for \(k\in \{1,\dots, n\}\), the sum of all \(k \times k\) principal minors is positive. A digraph \(D\) is said to have nonnegative \(Q\)-completion if every partial nonnegative \(Q\)-matrix specifying \(D\) can be completed to a nonnegative \(Q\)-matrix. For nonnegative \(Q\)-completion problem, necessary conditions and sufficient conditions for a digraph to have nonnegative \(Q\)-completion are obtained. Further, the digraphs of order at most four that have nonnegative \(Q\)-completion have been studied.