The utility model is an ink storage bursa and an ink box with an ink storage bursa. The ink storage bursa includes a bag-shape flexible bursa main body; a support element connected with an edge of the flexible bursa; an ink supply cavity provided with an ink injection inlet and an ink outlet. A one-way valve is arranged inside of the ink cavity, which includes a valve seat, a valve cover and a valve body. The ink box with an ink storage bursa includes an ink storage bursa and a shell. The ink storage bursa and the ink box with an ink storage bursa can effectively prevent ink leakage from printing head.