This work searches for the candidates of Galactic disk star clusters in Gaia Early Data Release 3 (Gaia EDR3) and determines their basic parameters from color-magnitude diagrams (CMDs). A friends-of-friends method for membership determination and stellar population models including binary stars (ASPS) and rotating stars are adopted. As a result, 868 new star cluster candidates are found, besides 2729 known ones. When checking the CMD of each candidate, 61 new candidates show main sequences including a turnoff, which suggests that they are real star clusters. The basic parameters, including distance modulus, color excess, metallicity, age (or age range), primordial binary fraction, and rotating star fraction, are determined carefully by fitting the morphologies of CMDs of 61 newly identified star clusters and 594 known star clusters, which have relatively clear main sequences. The CMDs are fitted in considerable detail to ensure the reliability of property parameters of clusters. All final results are included in a new star cluster catalog, which is named LI team's Star Cluster (LISC), and the catalog is available in the Zenodo repository.