The growth rate of cosmic structure is a powerful cosmological probe for extracting information on the gravitational interactions and dark energy. In the late-time Universe, the growth rate becomes nonlinear and is usually probed by measuring the two-point statistics of galaxy clustering in redshift space up to a limited scale, retaining the constraint on the linear growth rate f. In this paper, we present an alternative method to analyze the growth of structure in terms of local densities, i.e., f(Δ). Using N-body simulations, we measure the function of f(Δ) and show that structure grows faster in high-density regions and slower in low-density regions. We demonstrate that f(Δ) can be modeled using a log-normal Monte Carlo random walk approach, which provides a means to extract cosmological information from f(Δ). We discuss prospects for applying this approach to galaxy surveys.