In recent years it has become increasingly popular to use phylogenetic comparative methods to investigate heterogeneity in the rate or process of quantitative trait evolution across the branches or clades of a phylogenetic tree. Here, I present a new method for modeling variability in the rate of evolution of a continuously-valued character trait on a reconstructed phylogeny. The underlying model of evolution is stochastic diffusion (Brownian motion), but in which the instantaneous diffusion rate ([sigma].sup.2 ) also evolves by Brownian motion on a logarithmic scale. Unfortunately, it's not possible to simultaneously estimate the rates of evolution along each edge of the tree and the rate of evolution of [sigma].sup.2 itself using Maximum Likelihood. As such, I propose a penalized-likelihood method in which the penalty term is equal to the log-transformed probability density of the rates under a Brownian model, multiplied by a 'smoothing' coefficient, [lambda], selected by the user. [lambda] determines the magnitude of penalty that's applied to rate variation between edges. Lower values of [lambda] penalize rate variation relatively little; whereas larger [lambda] values result in minimal rate variation among edges of the tree in the fitted model, eventually converging on a single value of [sigma].sup.2 for all of the branches of the tree. In addition to presenting this model here, I have also implemented it as part of my phytools R package in the function multirateBM. Using different values of the penalty coefficient, [lambda], I fit the model to simulated data with: Brownian rate variation among edges (the model assumption); uncorrelated rate variation; rate changes that occur in discrete places on the tree; and no rate variation at all among the branches of the phylogeny. I then compare the estimated values of [sigma].sup.2 to their known true values. In addition, I use the method to analyze a simple empirical dataset of body mass evolution in mammals. Finally, I discuss the relationship between the method of this article and other models from the phylogenetic comparative methods and finance literature, as well as some applications and limitations of the approach.