To provide a thermoplastic elastomer composition which extremely reduces the bleeding of a softening agent for nonaromatic rubbers in spite of ultra-low hardness and has a small compression set, and a molded product thereof.

The thermoplastic elastomer composition includes (A) 100 pts.mass hydrogenated block copolymer which is obtained by hydrogenating a block copolymer comprising at least one polymer block mainly having a vinyl aromatic compound and at least one polymer block mainly having a conjugated diene compound and has a weight average molecular weight of 300,000-450,000, (B) 180-270 pts.mass softening agent for nonaromatic rubbers having a kinematic viscosity at 40°C of 350-400 mm2/sec and a molecular weight distribution (Mw/Mn) measured by the gel permeation chromatography of not greater than 1.3, and (C) 3.0-10 pts.mass polypropylene, and has a Shore A hardness of 4-12°.