From April to July 2018, a data sample at the peak energy of the γ(4S) resonance was collected with the Belle II detector at the SuperKEKB electron-positron collider. This is the first data sample of the Belle II experiment. Using Bhabha and digamma events, we measure the integrated luminosity of the data sample to be (496.3 ± 0.3 ± 3.0) pb-1, where the first uncertainty is statistical and the second is systematic. This work provides a basis for future luminosity measurements at Belle II. © 2019 Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Sciences and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.