On a compact oriented Riemannian manifold a critical metric is a critical point in the space of metrics of the \(L^ 2\)-norm of the curvature tensor. In particular every Einstein metric on a compact 4-dimensional manifold is critical. The main result of the paper is a compactness theorem for critical metrics on a compact 4-dimensional manifold with a lower bound for the Ricci curvature and the injectivity radius and an upper bound for the diameter and the \(L^ 2\)-norm of the Ricci curvature. This extends compactness results for Einstein metrics on compact 4-dimensional manifolds due to \textit{L. Z. Gao} [J. Differ. Geom. 32, No. 1, 155-183 (1990; Zbl 0719.53024)].