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In the light of the recent works by Sen (hep-th/0203211, hep-th/0203265, hep-th/0204143) and Gibbons (helth/0204008), we present a phase-plane analysis on the cosmology containing a rolling tachyon field in a potential resulting from string theory. We show that there is no stable point on the phase-plane, which indicates that there is a coincidence problem if we consider the tachyon as a candidate for quintessence. Furthermore, we also analyse the phase-plane of the cosmology containing a rolling tachyon field for an exactly solvable toy potential in which the critical point is stable. Therefore, it is possible for the rolling tachyon to be a candidate for quintessence if we give up the strict constraint on the potential or find a more appropriate effective potential for the tachyon from M/string theory.