Construction will begin Wednesday on a 300-foot pedestrian tunnel connecting the Court House Metro station in Arlington with an office project across Wilson Boulevard, county officials said yesterday. Work on the project is expected to snarl traffic and aggravate parking around the courthouse.

The tunnel, to a plaza at the Colonial Place office project, is expected to be finished by December, said William C. Scruggs, chief of Arlington's traffic engineering division. The tunnel, however, will not be opened until the first Colonial Place office building opens in early 1986.

Details of the tunnel were among the compromises shaped in negotiations between the county and the site owners, Mobil Land Development Corp. The county initially wanted the tunnel to end in one of the Colonial Place buildings, but later agreed to outdoor access from the plaza, Scruggs said.

Greg Friess, executive vice president and general manager of Colonial Village Inc., also a subsidiary of Mobil Corp., declined yesterday to give the cost of the project, which the corporation is financing.

County officials insisted the tunnel be built. "This is something [the county] has wanted for a long time," Scruggs said. "It should encourage the use of Metro. It helps reduce traffic. It lets pedestrians cross a busy street with ease. In bad weather, it's more pleasant for pedestrians to walk in a tunnel."

For the rest of this year, though, the construction will mean fewer parking spaces and more detours near the courthouse, where redecking of a bridge linking Arlington Boulevard (Rte. 50) and Courthouse Road already has created traffic problems.