The demand comes largely from Latin America and the Middle East, regions that have a healthy appetite for 4G networks but not necessarily the cash to splash on Apple's iPhones, for example.
Shipments in some of those emerging markets have doubled or even tripled.
Huawei said in a statement it shipped smartphone 34.3 million units in the first half of this year, boosted by sales of its flagship phones the Ascend Mate 2 and the Ascend P7, both high-spec models.
The second quarter saw it ship 20.6 million units - an 85% year-on-year increase.
Other Chinese vendors are also reporting booming smartphone sales, but Huawei ships a higher proportion of its production to foreign markets, said Melissa Chau, an analyst with research firm IDC.
"It has the most number of shipments outside of China, roughly 40%," she estimated. "If you look at Lenovo, ZTE, or Xiaomi, they are nowhere near that."
"Despite a challenging quarter for Samsung, and to a lesser extent Apple, the strong market demand boosted results for most smartphone vendors," IDC said in a statement.
"Emerging markets supported by local vendors are continuing to act as the main catalyst for smartphone growth. Among the top vendors in the market, a wide range of Chinese OEMs more than outpaced the market in 2Q14. By far the most impressive was Huawei, nearly doubling its shipments from a year ago, followed by another strong performance from Lenovo."
“Across Europe there is an accelerating trend of fragmentation in the handset market as smaller brands gain real traction,” said Dominic Sunnebo, Strategic Insight Director, Kantar Worldpanel ComTech.
“...Newcomers to the European market such as Huawei...are challenging the established names.”
In the second half of the year, Huawei said it will continue to :commit to the development of the 4G LTE market, designing and developing innovative technologies for its range of consumer devices." In addition to further enhancing collaboration with telecommunication carriers, open market and online sales channels, it aims to put more new premium mid- to high-end flagship 4G LTE-enabled smart devices and wearables into the hands of consumers worldwide.
Earlier this month, Richard Yu, the head of Huawei's consumer business group, said in an internal memo that revenue for his group, which mainly sells smartphones, rose 30% in the first half of this year. Yu also said in the memo, as reported by the Wall Street Journal, that his group by midyear had already achieved more than half of its 2014 profit target.