The car insurance market is “dysfunctional” and does not reward loyal customers, said the chief executive of Aviva, Mark Wilson.
He said firms were tempting in new customers with prices that were “too low”, which put prices up for existing customers.
Car insurance premiums have gone up by 11% in the last year, according to the Association of British Insurers (ABI).
The typical bill for an annual policy is now £484, it said.
“I think that the UK car insurance market is dysfunctional, I don’t think it works properly,” Mr Wilson told the BBC’s Today Programme.
“The entry level is too low and then it gets put up for all existing customers,” he said.
Aviva has developed a “suite” of products to be launched before the end of the year, which will help reward loyal customers.
“Let’s see how it goes,” Mr Wilson said.
Car insurance is just 2% of Aviva’s total business.
Shares in Aviva rose by about 0.5%, after the company reported operating profits up by 8% in the first half of 2017.
Sales of annuities, bulk annuities and equity release products all rose, with growth particularly strong in the UK.
The dividend was up by 13%.
However, Mr Wilson refused to say whether he thought he was paid too much.
“I think I’ll let the shareholders answer that one,” he told the BBC.
He said the company was happy to publish the ratio of its highest paid employee to its lowest, as soon as the government had determined how such a ratio should be expressed.
Aviva already pays its employees the National Living Wage and requires all its contractors to do likewise.