Britain’s third-largest pharmaceuticals company beat analysts’ predictions to record revenue of $1.09bn (£0.67bn) for the three months to September.
Predicted full-year profit figures have been rising, and the company is confident of meeting them.
Sales of Shire’s medicines treating Gaucher disease and Fabry disease, two rare genetic disorders, have been boosted by manufacturing problems at US rival Genzyme forcing patients to switch drugs.
Meanwhile ADHD treatment Vyvanse recorded a 32 per cent growth in sales, bringing in $200m in the period.
The growth was fuelled by rising prescription sales for hyperactivity drugs in the US, which increased by nine per cent in the quarter.
Successful trials of Vyvanse in Europe have provided the opportunity to gain regulatory approval in the market.
According to JPMorgan Cazenove analysts the drug could eventually claim 50 per cent of the maket for ADHD medicines.