The Cooper Gallery has been awarded more than £46,000 to develop a project to increase the number of visitors.
The Creating Connections project could transform the gallery, and also seeks to enable more people to engage with its heritage and stories.
The gallery, on Church Street, celebrates its centenary next year and attracts about 50,000 visitors a year.
The development grant has been awarded to help the gallery progress its plans to apply for a full grant for the project, of just under £635,000, at a later date.
The project plans to extend the gallery spaces to allow more of the collection of historic works of art to be displayed, make the gallery more interactive and fun, work with schools, alter the building's layout to restore the original entrance and improve the outdoor public space at the rear.
It will also improve artwork storage and conserve works of art for display and to provide opportunities for more people to get involved through volunteering.
The gallery is managed on behalf of the trustees by Barnsley Council's Arts and Museums Service and the project is a partnership between the Cooper Gallery trustees and the council.
Specialists will now be appointed to help develop the plans before a round two bid is submitted later this year.
The Cooper Gallery opened in 1914 and is home to a collection of more than 400 historic works of art donated by wealthy Barnsley industrialists.
Paul Elmhirst, chairman of the Cooper Gallery trustees, said: "We are delighted to be partners in this ambitious project which has just won the backing of the Heritage Lottery Fund.
"As well as improving the facilities of the gallery the project will provide a focus for celebrating the centenary of the Cooper Art Gallery and the foresight of those remarkable Barnsley benefactors who made it possible."
Coun Linda Burgess, culture spokesman, said the project would focus on the stories of the collectors, many of whom were local figures during Barnsley's industrial age.
She added: "Creating Connections will enable more visitors to appreciate the heritage of the gallery's collection of historic artwork and the collectors themselves.
"The Cooper plays an important role in the cultural life of the borough and, if successful with the second round application, the Creating Connections project will transform the gallery, making it an even more important part of the wider visitor offer in Barnsley."