West Sussex County Council said work was scheduled to begin this spring, but had to be postponed while the bridge design and figures were reviewed.
The authority said the £5.8m budget was based on estimates but the costs of the work had increased by the time construction was planned to go ahead.
The council said it was working to achieve the earliest start date.
Pieter Montyn, cabinet member for highways and transport, said: "The new footbridge will cost a significant sum of money to construct.
"The county council has a responsibility to ensure that we get value for money.  Therefore it is important that sufficient time is taken to check and agree the contract price for the construction of the bridge."
Work to build a footbridge in Shoreham has been delayed because the project costs have exceeded the £5.8m budget.