The group saw gross written premiums grow 3.3% in constant currency to 1.16 billion US dollars (£877.4 million) in the three months to March 31.
Hiscox recorded growth at its retail and London Market divisions, while reinsurance dipped.
In the London Market, rates have risen 4% this year with cargo, marine hull and US public company directors and officers seeing the largest increases.
Boss Bronek Masojada said: “We have done what we said we would do in the first quarter. In retail we continue to pull back in US private company D&O, where conditions are challenging, and the UK business is adapting to a new IT system which will help us capture the long-term opportunity.
“In the London Market and in reinsurance, where conditions are improving, we are growing in the right areas and maintaining our focus on writing profitable business.”
Hiscox is pencilling in growth for its retail businesses towards the mid-point of its 5%-15% target range in the second half of the year.
Last year the company was hit by a number of catastrophes such as the California wildfires and several hurricanes, typhoons and storms.
It said on Tuesday: “Due to heavy losses in the risk excess and the wildfire market over the last two years, we have taken action to adjust our view of risk, increase rates and reduce exposure on some business.”
It also said rates have risen at its reinsurance arm.
On Brexit, the group said that Hiscox Ireland and a number of European underwriting partnerships transferred from Hiscox UK to Hiscox Europe as part of the structural changes made in readiness for Britain’s EU departure.
The insurer has also increased its presence in Dublin, with the Ireland business now integrated into its European operation.