Transit in Beijing from Taipei to U.S.

I am holding U.S. passport with tourist L (expires on June/20/13), my travel plan is going to Beijiing from U.S. on Jun/06 (joined 14 days tour) and from Beijing to Taiwan on June/20 and stay in Taiwan for 2 months returning to U.S. on Aug/20 from Taiwan through Beijing (Round trip ticket on Air China from U.S. to Beijing with stop over in Taipei).
Do I need visa from Taipei via Beijing back to U.S. (about 5 hours lay-over in Beijing) since my Chinese L type one will be expired.