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The anisotropy of two successive transitions of the spin-ladder compound LiCu2 O2 is studied by the specific heat (C) under magnetic fields with H// c and H// ab (written as Hc and Hab in the following) up to 14 T. The peak of specific heat at 24.5 K in zero field shifts to lower temperature when the field is increased and the magnitude of the peak is suppressed by the field. On the contrary, the peak of 22.5 K shifts to higher temperature, especially at 14 T. Its magnitude increases in the field of Hc, whereas it decreases in the field of Hab. We calculate the entropy change between 21 K and 63 K. The different influence of the spin ordering by fields of different direction is obtained. Our experimental results suggest a mixed state between the long range incommensurate helimagnetic ground state and the higher-T short-range dimer liquid state. The temperature range of mixed state is shrunk with the increasing field. Possible mechanism is discussed.