We report a giant zero field cooled exchange bias (ZEB) effect (~0.65 T) in La1.5Sr0.5CoMnO6 sample. Magnetic study has revealed a reentrant spin glass ~90 K, phase separation to spin glass and ferromagnetic phases below 50 K and canted antiferromagnetic transition ~10 K. A small conventional exchange bias (CEB) is established with the advent of spontaneous phase separation down to 10 K. Giant ZEB and enhanced CEB effects are found only below 10 K and are attributed to the large unidirectional anisotropy at the interface of isothermally field induced ferromagnetic phase and canted antiferromagnetic background.