Data are presented on the activity of supported vanadium-magnesium catalysts (VMCs) with different vanadium content in ethylene polymerization and the molecular weight characteristics of the produced polyethylene. The VC1 catalyst, with a very low vanadium content (0.12 wt.%), showed a sixfold higher activity per unit weight of vanadium than the VC2 catalyst with a high-vanadium content (4.0 wt.%). Additionally, the total activity of VC2 (kg PE/g cat·h) was fivefold higher when compared to VC1. The introduction of hydrogen in polymerization leads to a considerable decrease in the activity of both catalysts. The polyethylene obtained in the presence of hydrogen over both catalysts has a broad bimodal molecular weight distribution (MWD) with a distinct shoulder in the high-molecular region (Mw ≥ 106 g/mol). Decomposition of the MWD curves of bimodal polyethylene into two fractions (high- and low-molecular fractions) made it possible to determine for the first time the ratio of the reaction rate constants of chain transfer with hydrogen (KtrH) and polymer chain propagation (Kp) for two groups of the VMC active sites producing low- and high-molecular fractions of bimodal polyethylene.