Exchange-bias (Hex) of NiFe/NiO bilayers grown epitaxially on MgO(100) and MgO(111) have been measured in order to understand exchange biasing phenomena more clearly. According to HRXRD, the separate reflections of MgO and NiO were observed, which implied that NiO layers grew epitaxially on MgO substrates. The rms roughness (Rrms) of NiO on MgO(100) measured by AFM was 1.79 Å while that of NiO on MgO(111) was 17.85 Å. Despite a higher Rrms, the value of Hex, 85 Oe in the case of NiFe/NiO on MgO(111) was larger than that of NiFe/NiO on MgO(100), 47 Oe, probably due to stronger effect of (111) texture of NiO surface. But low Hex of NiFe/NiO on MgO(111) implied that exchange biasing was generated by not only upcompensated spins but also compensated spins of NiO. Hex of NiFe/NiO bilayer grown on Si(100) was 118 Oe. According to SEM, grain size of NiO surface grown on Si(100) was very small, which mean its domain size was also very small. The explanation of the effect of domain size was consistent with random field model.