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Aims.We inspect the microlensing data of the KMTNet survey collected during the 2018-2020 seasons in order to find lensing events produced by binaries with brown dwarf (BD) companions. Methods.In order to pick out binary-lens events with candidate BD lens companions, we conducted systematic analyses of all anomalous lensing events observed during the seasons from 2018 to 2020. By applying a selection criterion of mass ratio between the lens components of 0.03 ≲q≲ 0.1, we identify four binary-lens events with candidate BD companions, namely KMT-2018-BLG-0321, KMT-2018-BLG-0885, KMT-2019-BLG-0297, and KMT-2019-BLG-0335. For the individual events, we present interpretations of the lens systems and measure the observables that can be used to constrain the physical lens parameters. Results.The masses of the lens companions estimated from the Bayesian analyses based on the measured observables indicate high probabilities that the lens companions are in the BD mass regime; that is, 59%, 68%, 66%, and 66% for the four respective events.