Litton Properties claims its proposals for a food store at Riverside Business Park, in Bakewell, were not fully considered when the Aldi application was approved in May.
The Aldi application is for a food store at the former Cintride factory site, on Buxton Road, which is adjacent to Riverside Business Park.
The Litton proposals – which were submitted in April – include a retail outlet, hotel, and bridge over the River Wye, at the business park.
A spokesman for Litton, which owns Riverside, said its scheme could only be delivered with funding from a major food store.
The spokesman said: “We have no fundamental problem with Aldi’s proposal. Our objection and concerns are with the fact that our proposals were not considered at the same time.
“There was no comparison available to members of the planning committee for them to decide fairly the most appropriate location if there will be only one new food store in Bakewell.
“As such, we don’t feel our proposals have been treated fairly and so are seeking a judicial review to determine if the Peak Authority’s decision was unlawful.”
John Scott, director of planning, said the authority intends to defend the decision.
Mr Scott said: “The [Aldi] application was submitted in January 2015 and was approved unanimously at its planning committee in May 2015.
“At that committee, the members were given a very thorough explanation of the proposals by Litton Properties... including a new food store.
“The authority is currently considering two applications for redevelopment of the business park, including retail development and a hotel. These were submitted in April 2015.”
A spokesperson for Aldi said: “We feel that the actions of Litton Properties are unfortunate as they will, at the very least, result in additional delays and costs to the delivery of the permitted Aldi foodstore.
“At worst, depending on the outcome of the process, the multi-million pound Aldi investment in Bakewell could be threatened.”