Let \(G\) be a reductive group over the field of complex numbers. The aim of this paper is to construct a compactified moduli space of principal \(G\)-bundles on a smooth manifold \(X\). The author fixes a faithful representation \(G \to \text{SL}(V)\), \(V\) being a complex vector space of dimension \(r\). Giving a principal \(G\)-bundle is equivalent to giving a vector bundle \(A\) together with a section of \(\text{Iso} (A, V^{\vee}\otimes {\mathcal O}_X)//G\). The author defines a singular principal bundle as a pair \((A, \sigma)\) where \(A\) is a torsionfree sheaf of rank \(r\) with a trivial determinant and \(\sigma\) is a section of \(\text{Hom} (A, V^{\vee}\otimes {\mathcal O}_X)//G\). Projective coarse moduli schemes of singular principal \(G\)-bundles are constructed. Compactified moduli spaces for principal \(G\)-bundles on \(X\) are also constructed by different methods by T. L. Gomez and I. Sols [“Moduli space of principal sheaves over projective varieties”, http://front.math.ucdavis.edu/math.AG /0206277]. The author uses the moduli of tensor fields constructed by T. L. Gomez and I. Sols [“Stable tensors and moduli space of orthogonal sheaves”, http://front.math.ucdavis.edu/math.AG /0103150].