We present a nonparametric method for estimating scale-free graphical models. To avoid the usual Gaussian assumption, we restrict the graph to be a forest and build on the work of forest density estimation. The method is motivated from a Bayesian perspective and is equivalent to finding the maximum spanning tree of a weighted graph with a log degree penalty. We solve the optimization problem via a minorize-maximization procedure with Kruskal's algorithm. Simulations show that the proposed method outperforms competing parametric methods, and is robust to the true data distribution. It also leads to improvement in predictive power and interpretability in two real data examples.