Large-sample or population-level sequencing data provide unprecedented opportunities for inferring detailed population histories, especially recent demographic histories. On the other hand, it challenges most existing population genetic methods: Simulation-based approaches require intensive computation, and analytical approaches are often numerically intractable when the sample size is large. We propose a computationally efficient method for simultaneous estimation of population size, the rate, and onset time of population growth in the very recent history, using the pattern of the total number of segregating sites as a function of sample size. Coalescent simulation shows that it can accurately and efficiently estimate the parameters of recent population growth from large-scale data. This... approach has the flexibility to model population history with multiple growth stages or other epochs, and it is robust when the sample size is very large or at the population scale, for which the Kingman’s coalescent assumption is not valid. This approach is applied to recently published data and estimates the recent population growth rate in the European population to be 1.49% with the onset time 7.26 ka, and the rate in the African population to be 0.735% with the onset time 10.01 ka.