The company said turnover rose 23% to £7.5bn in the three months to 30 September compared to a year earlier, while core operating profit jumped 35% to £2.3bn over the same period.
A weak pound was a major driver of earnings growth last quarter, as the multinational firm benefits from income in stronger foreign currencies.
Sterling has lost nearly 20% of its value against the US dollar since the EU referendum in June.
However, earnings were much more muted once stripped of currency fluctuations. Turnover at constant exchange rates only grew 8%, while core operation profit rose 13%.
The company has maintained a positive outlook in recent months, despite market fears surrounding Brexit.
Shortly after the referendum, Glaxo announced it was pumping £275m into three British manufacturing sites - dubbing the UK an "attractive location"
In its latest trading update, Glaxo chief executive Sir Andrew Witty said the company was on track to meet its earning target for 2016.
He said: "Our third quarter results reflect strong performances across the group and the sustained progress we have made over the course of 2016 to deliver sales growth of new products, maintain effective cost control and execute on our restructuring and integration plans."
He added: "Our most recent review of the group's pipeline reinforces our confidence in the near-term portfolio and the options we have in early-to-mid stage development.
The latest set of earnings will be one of the last overseen by Sir Andrew.
Glaxo last month named consumer healthcare boss Emma Walmsley as its new chief executive to replace Sir Andrew when he retires and steps down in March 2017.