Skyscraper was bred at Woburn Abbey by Francis Russell, 5th Duke of Bedford, who was only 21 years old when the horse was foaled.

At the Newmarket Second Spring meeting he won the Prince's Stakes (one hundred guineas each), beating Earl Grosvenor's Brother to Skylark, Lord Clermont's Pipator, and six others.

[1] At Epsom on 28 May he won the Derby, beating a field of ten which included Sir George, Brother to Skylark, and the Prince of Wales's Soujah ul Dowlah.

[5] While at Epsom he also collected seventy guineas from the Earl of Egremont's three-year-old filly Tag, on whom Sam Chifney won that year's Oaks.

[1] At the Newmarket first Spring meeting Skyscraper won the Jockey Stakes (100 guineas each), beating Skylark, Pipator, and Pickle.

At the Newmarket second Spring meeting he took on Sir Charles Bunbury's Glaucus in a match for one thousand guineas and was beaten.

At Lewes he was runner-up for the King's Plate to the Earl of Egremont's Precipitate (1787), and at Derby he walked over in a race for fifty guineas.

At the Newmarket first Spring meeting he was runner-up for the King's Plate to Coriander, one of the horses he had beaten in the same race the year before.

[1] His offspring included: [1] After he won the Derby, Skyscraper's portrait was painted by J. N. Sartorius, and this was later engraved in mezzotint by Houston.