Lei Jun, who is also co-founder of the tech firm, made the projection on Sina Weibo, China's most widely used microblogging site, and it was reposted on Xiaomi's website.
"We again promise, we will at least supply 40 million phones in 2014!" he wrote. China is the world's biggest market for smartphones.
Lei said privately held Xiaomi had sold 18.7 million smartphones in 2013, a 160 percent increase from 2012, and that sales revenues, including taxes, rose 150 percent to 31.6 billion yuan.
Xiaomi's sales growth far exceeds projections for the global smartphone market, which is seen expanding at an annual rate of 18 percent a year until 2016, according to research firm Canalys.
Xiaomi's cheap yet sleek phones are popular in China, where Samsung Electronics remains the market leader. Xiaomi's handsets sell for between $130 and $410, much lower than the $740 price tag for the least expensive iPhone 5c model or a Samsung Galaxy Note II, which can retail for $570.
Xiaomi even managed to briefly rank sixth by market share in the second quarter of 2013, one notch above Apple.
Apple is poised to boost its sales in China after it signed last month a deal with China Mobile Ltd, the world's largest mobile carrier by subscriber numbers. The deal could generate $3 billion in revenue in 2014 for the U.S. firm.
© Thomson Reuters 2014