Superclusters of galaxies mark the large-scale overdense regions in the Universe. Superclusters provide an ideal environment to study structure formation and to search for the emission of the intergalactic medium such as cosmic filaments and WHIM. In this work, we present the largest-to-date catalog of X-ray-selected superclusters identified in the first SRG/eROSITA All-Sky Survey (eRASS1). By applying the Friends-of-Friends (FoF) method on the galaxy clusters detected in eRASS1, we identified 1338 supercluster systems in the western Galactic hemisphere up to redshift 0.8, including 818 cluster pairs and 520 rich superclusters with ≥3 members. The most massive and richest supercluster system is the Shapley supercluster at redshift 0.05 with 45 members and a total mass of 2.58 ± 0.51 × 1016M⊙. The most extensive system has a projected length of 127 Mpc. The sizes of the superclusters we identified in this work are comparable to the structures found with galaxy survey data. We also found a good association between the eRASS1 superclusters and the large-scale structures formed by optical galaxies. We note that 3948 clusters, corresponding to 45% of the cluster sample, were identified as supercluster members. The reliability of each supercluster was estimated by considering the uncertainties in the redshifts of the galaxy clusters and the peculiar velocities of clusters. Furthermore, 63% of the systems have a reliability larger than 0.7. The eRASS1 supercluster catalog provided in this work represents the most extensive sample of superclusters selected in the X-ray band in terms of the unprecedented sample volume, sky coverage, redshift range, the availability of X-ray properties, and the well-understood selection function of the parent cluster sample, which enables direct comparisons with numerical simulations. This legacy catalog will greatly advance our understanding of superclusters and the cosmic large-scale structure.