Inferring the ancestral dynamics of effective population size is a long-standing question in population genetics, which can now be tackled much more accurately thanks to the massive genomic data available in many species. Several promising methods that take advantage of whole-genome sequences have been recently developed in this context. However, they can only be applied to rather small samples, which limits their ability to estimate recent population size history. Besides, they can be very sensitive to sequencing or phasing errors. Here we introduce a new approximate Bayesian computation approach named PopSizeABC that allows estimating the evolution of the effective population size through time, using a large sample of complete genomes. This sample is summarized using the folded allele frequency spectrum and the average zygotic linkage disequilibrium at different bins of physical distance, two classes of statistics that are widely used in population genetics and can be easily computed from unphased and unpolarized SNP data. Our approach provides accurate estimations of past population sizes, from the very first generations before present back to the expected time to the most recent common ancestor of the sample, as shown by simulations under a wide range of demographic scenarios. When applied to samples of 15 or 25 complete genomes in four cattle breeds (Angus, Fleckvieh, Holstein and Jersey), PopSizeABC revealed a series of population declines, related to historical events such as domestication or modern breed creation. We further highlight that our approach is robust to sequencing errors, provided summary statistics are computed from SNPs with common alleles. Molecular data sampled from extant individuals contains considerable information about their demographic history. In particular, one classical question in population genetics is to reconstruct past population size changes from such data. Relating these changes to various climatic, geological or anthropogenic events allows characterizing the main factors driving genetic diversity and can have major outcomes for conservation. Until recently, mostly very simple histories, including one or two population size changes, could be estimated from genetic data. This has changed with the sequencing of entire genomes in many species, and several methods allow now inferring complex histories consisting of several tens of population size changes. However, analyzing entire genomes, while accounting for recombination, remains a statistical and numerical challenge. These methods, therefore, can only be applied to small samples with a few diploid genomes. We overcome this limitation by using an approximate estimation approach, where observed genomes are summarized using a small number of statistics related to allele frequencies and linkage disequilibrium. In contrast to previous approaches, we show that our method allows us to reconstruct also the most recent part (the last 100 generations) of the population size history. As an illustration, we apply it to large samples of whole-genome sequences in four cattle breeds.