The scheme aims to transform the Italianate courtyard at the centre of the museum, which was constructed in the 19th century, into a modern piazza-style public space.
The redesign of the garden is part of a plan to transform the museum over the next 15 years. Under the plan the garden courtyard will be surrounded by new galleries. The scheme is being funded by the Friends of the V&A.
The six designs will be judged by a panel including architects Rick Mather, Charles Jencks and Eva Jiricna, consultant architect for the V&A Future Plan. A successful candidate will be selected in October, with work due to commence in October next year.
Director of the V&A Mark Jones said: "We are delighted that these six excellent designers have all agreed to submit new ideas for the garden. They give us a wide range of exciting designs from which to create a modern garden within a historic setting."