Citizens UK says moving from different countries and welcoming strangers is a strong part of both British and Christian history.
Their comments come as a report from University College London found immigrants from the European Economic Area (EEA) pay in more to the UK than they take out in benefits and public services.
They paid in £4.4bn more to the UK than they took out between 1995 and 2011.
The study also found immigrants who have arrived since 2000 were 43% less likely to receive state benefits than British people.
However, immigrants from outside the EEA cost the UK £118bn between 1995 and 2011.
British people cost the UK more than five times this figure, at £591bn.
Neil Jameson, the Executive Director of Citizens UK, told Premier's News Hour: "Yours is a Christian radio station, and the tradition of the stranger in biblical history and in the Gospels is to respect the stranger more than the people you know.
"Mostly we're fed myths, stereotypes and rumours, and this is the first concrete attempt by academics to put the balance right.
"These are young people, well educated people, who do not come here in order to milk the system, but come here to earn reasonable money, possibly send it home, and give a lot to the country.
"The Catholic Church is full of migrants - Britain is a country of migrants. If you look at our history we're made up of people who came from all over the world.
"It's counterproductive to say that just by being a migrant you're a problem. That's not been the case.
"It denies our history, it denies our heritage."
But the Chairman of Migration Watch, Sir Andrew Green, said:
"This report confirms that immigration as a whole has cost up to £150 billion in the last 17 years.
"As for recent European migrants, even on their own figures - which we dispute - their contribution to the exchequer amounts to less than £1 a week per head of our population."
The government's Immigration Minister James Brokenshire said the report does not highlight the stress that immigration puts on public services like schools and hospitals.
He also said immigration needs to decrease from hundreds of thousands of people to tens of thousands.
Prime Minister David Cameron is attempting to renegotiate the terms of Britain's membership of the European Union. Part of the change he's trying to achieve is to lower the amount of migrants who can come to the UK from member states.
Currently, there is no limit on the amount of people who move to the UK from member states.
However a spokesman for the German government said the free movement of people in the EU was "not negotiable."
David Cameron has also pledged to hold an in-out referendum on Britain's membership of the EU, if the Conservative Party is re-elected in next year's general election.