A related company, Home Park Properties which was formed in January 2010, has also been issued with a winding up petition by HMRC.
No one from the club was available to comment on the matter.
The club recorded a £2.8m loss for the 2008/09 financial year and were previously issued with a winding-up order for unpaid tax by HM Revenue & Customs last season.
Former Leeds and Cardiff chairman Peter Ridsdale was in Plymouth on Thursday holding talks with the Argyle board.
On the pitch, Argyle sit 15th in League One, just three points above the relegation zone, and just 4,960 fans watched them beat Dagenham & Redbridge 2-1 on Tuesday, their lowest gate of the season.
Source: BBC Sport
Source: BBC Sport