A propylene/1-butene random copolymer containing 60 to 90 mol % of propylene units and 10 to 40 mol % of 1-butene units and has a triad isotacticity of not less than 85% and not more than 97.5%, a molecular weight distribution of from 1 to 3, an intrinsic viscosity of from 0.1 to 12 dl/g, a melting point of from 40 to 75.degree. C. and a crystallization rate at 45.degree. C. of 10 minutes or less, and satisfying the following relation, 146 exp (-0.022M).gtoreq.Tm.gtoreq.125 exp (-0.032M), and an olefin catalyst for preparation thereof.