MasterQuote Insurance Services is offering insurance quotations to motorists who have previous convictions for driving offences such as speeding.
The insurance provider said that this could help reduce the number of uninsured drivers currently on the UK's roads.
The Motor Insurers Bureau pays out around £129 million in settlements for victims of uninsured motorists each year.
MasterQuote managing director Sandy Dunn said: "Many drivers who have motor convictions try to get insurance but cannot find anyone who will cover them. Most of these motorists have committed just one offence and have no intention of re-offending. This tempts them to drive without insurance."