Most of the new staff will be added in China.
"We will increase our staff to between 33,000 and 35,000 by 2020," Stefan Jacoby told Automotive News Europe magazine.
The company currently employs around 24,000 people worldwide -- around 16,000 in Sweden, 5,000 in Belgium and 1,000 in China as well as 2,000 in other countries.
Jacoby said Volvo aimed to sell 800,000 vehicles per year by 2020, one-quarter of them in China, now the world's biggest auto market.
In 2010, Volvo sold about 374,000 vehicles worldwide, with sales rising by 29 percent in northern Europe and 36 percent in China.
Geely bought Volvo from Ford last year.
While Sweden's other major car brand, Saab, continues its battle to escape bankruptcy, Volvo's announcement is a clear statement of intent.
The Local reported in October that Geely had approached Saab's reconstructor, lawyer Guy Lofalk to express an interest.
According to reports in the Dagens Nyheter daily, Geely has been watching Saab's struggles with interest, but has stayed cautious about entering the fray.
The firm refused however to confirm the reports and with Saab's bankruptcy protection set to be lifted in December the speculation has cooled off.