A polyethylene composition comprising a mixture of three kinds of polyethylenes (A), (B) and (C) characterized in that:(i) the viscosity average molecular weight of (A) is 1,000-100,000, the viscosity average molecular weight of (B) is 100,000-1,000,000, the viscosity average molecular weight of (C) is 400,000-6,000,000, the molecular weight ratio of (B) to (A), i.e. B/A, is 2-200 and the molecular weight ratio of (C) to (B), i.e. C/B, is 1.5 or more.(ii) the mixing ratio of (A) to (B) is 30/70 to 70/30 and the mixing ratio of (C) is 1-10% by weight based on the total composition, and(iii) the melt index of the composition is 0.001-1, and a process for producing said composition. This polyethylene composition is excellent in physical properties in that it has an appropriate die swell, a high melt tension and an excellent moldability and exhibits a high stiffness and a high ESCR.