This offset a slump in tourism following attacks blamed on Islamist militants.
Gross domestic product rose 5.8 per cent from a year earlier in the three months through June and increased 4.0 per cent on a seasonally adjusted quarterly basis, the statistic's office said on Monday.
(READ MORE: Kenyan tourism faces negative impact due to domestic terrorism)
In the first quarter it had expanded 4.4 per cent from a year earlier, revised to take account of a recent rebasement of GDP, and 2.7 per cent on a quarterly basis.
Tourism, however, has been badly affected this year by a number of bombings in tourist areas on the coast and elsewhere, which were blamed on Islamist militants and prompted some Western countries to warn against travel to Kenya.
Output from the accommodation and restaurant sector slumped 18.6 per cent in the second quarter from a year earlier, the data showed.
(READ MORE:British tourists to bring relief to Kenya's strained tourism sector)
The slump in tourism means Kenya's economy will slow this year. Finance Minister Henry Rotich has already cut the government's 2014 growth forecast to 5.3-5.5 per cent from an initial 5.8 per cent, citing "challenges", without offering specifics.
Last year the economy grew 5.7 per cent, taking the rebasement into account.
The rebasement of GDP last month increased the size of the Kenyan economy by about 25 percent, pushing it into the top 10 African economies.
Construction output rose by 18.9 per cent during the second quarter from a year earlier, manufacturing grew 9.1 per cent while financial and insurance services increased by 8.3 per cent, the data showed.
Agricultural output slowed down, though, rising by 5.5 per cent from a year earlier, after 5.9 per cent growth in the first quarter.