We report the observation of exchange bias phenomena in the hole-doped perovskite cobaltite La0.88Sr0.12CoO3 in which a spontaneous phase separation occurs. When the sample is cooled in a static magnetic field through a freezing temperature, the magnetization hysteresis loops shift to the negative field. Moreover, the exchange bias strongly depends on the cooling field. These results highlight the important role of a glassy interface between the intrinsic inhomogeneous phases in a phase-separated system.