A process for producing a modified polypropylene having a very high melt tension and superior stiffness and moldability, and a molded product obtained by using the modified polypropylene are provided.which process includes adding 0.05 to 10 millimols of a cross-linking auxiliary to 100 g of a linear polypropylene, mixing them, irradiating ionizing radiations to the mixture so as to give an absorbed dosage of 1 to 20 kGy, and successively heat-treating the resulting material at 80.degree. to 350.degree. C.,which modified polypropylene has(A) a degree of branching of substantially 1,(B) a relationship between its melt tension (MS) at 230.degree. C. and its intrinsic viscosity (.eta.) measured in tetralin at 230.degree. C. expressed by an inequalitylog (MS)>4.24.times.log [.eta.]-0.915, and(C) a percentage of extraction residue in boiling xylene of 1% by weight or less.