"concern grew" is correct and can be used in written English. You could use it to show that a feeling of anxiety or worry is increasing. For example: "As the environmental crisis worsened, concern grew among citizens.".
Today, concern grew exponentially.
When Philby managed to escape to Moscow, concern grew.
When concern grew, prominent European voices started openly sending warnings.
As the March general election approached, concern grew of an Eta bombing campaign.
The concern grew when Iraq laid down the boundaries of the off-limits areas.
When reports began arriving from Scotland that addicts had started dying mysteriously, concern grew.
As concern grew that the skin of Florida's bubble was tearing, nature provided a drawing-pin of its own.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union