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We construct the effective action of a $D_p$-brane-anti-$D_p$-brane system bymaking use of the non-abelian extension of tachyonic DBI action. We succeed theconstruction by restricting the Chan-Paton factors of two non-BPS $D_p$-branesin the action to the Chan-Paton factors of a $D_p\bar{D}_p$ system. For thespecial case that both branes are coincident, the action reduces to the oneproposed by A. Sen. \\The effective $D_p\bar{D}_p$ potential indicates thatwhen branes separation is larger than the string length scale, there are twominima in the tachyon direction. As branes move toward each other under thegravitational force, the tachyon tunneling from false to true vacuum may make abubble formation followed by a classical evolution of the bubble. On the otherhand, when branes separation is smaller than the string length scale, thepotential shows one maximum and one minimum. In this case, a homogeneoustachyon rolling in real time makes an attractive potential for the branesdistance. This classical force is speculated to be the effective force betweenthe two branes.Comment: Latex, 14 pages, 1 figure, the version appears in JHE

D-brane anti-D-brane effective action and brane interaction in open string channel