Try has given Blue Star Garages, which owns most of the shares in the struggling first division outfit, two weeks to come up with the £435 000 it claims it is owed for building the 4500-seat north stand at the Fratton Park ground in 1997.
The stand has been the subject of 18 months of wrangling between the club and the contractor.
A hearing to consider Try's winding-up request will take place in the High Court on 20 January.
The order comes as a blow to the 116-year-old club, delaying takeover talks between its owner and a buyout consortium.
Try had built the main part of the stand by October 1997 but withdrew after the club ran into financial difficulties at the end of the year.
We regret having to take this sort of action against any company. We are not interested in taking legal action – all we are interested in is getting paid
Richard Barraclough, company secretary, Try
Try company secretary Richard Barraclough said his company agreed to a rescheduled payment plan in January 1998, with Blue Star Garages acting as guarantor. However, payments had stopped by mid-1998 and Try won a High Court order for the outstanding sum in November.
Barraclough said the winding-up order is a last resort.
He said: "We regret having to take this sort of action against any company. We are not interested in taking legal action – all we are interested in is getting paid what we are owed." In July last year, Portsmouth FC issued a counter-writ against Try claiming £356 850 damages plus interest for negligent misrepresentation and £70 000 plus VAT to rectify defects on the stand and terrace canopy.
Stadium manager David Watson said: "A lot of the work Try carried out did not meet the original specifications in the contract.
"As far as I'm aware, we are still pursuing our original claim." Portsmouth employed teams of subcontractors to finish off major works, including the fitting out of facilities beneath the stand and groundworks.