Layered transition metal oxide PbPdO2 has great potential application in electronic devices because of its unique electronic structure and large thermoelectric power at room temperature. In this work, strain effect on the electronic structure of PbPdO2 slab with preferred (0 0 2) orientation was systematically investigated using first-principles calculation. The calculated results indicate that PbPdO2 ultrathin slab possesses a small indirect gap while an indirect-direct band gap transition occurs when a moderate 2% compression or tensile strain is applied on the slab. Moreover, this strain induced indirect-direct band gap transition was analyzed in detail using the charge density difference at different point of valence band. The charge transfer and energy barrier with charge polarization resulting from the changes of bond length and angle for Pd-O bonding under the strain, have been accounted for this transition. Remarkablely, for the (0 0 2) preferred orientation PbPdO2 slab, the predicted carrier mobilities of electrons and holes are 11 645.31 and 694.60 cm2 V-1 s-1 along the x-axis direction, 935.05 and 16.05 cm2 V-1 s-1 along the y -axis direction, respectively. These calculated mobilities of electrons along the x-axis direction are larger than those for 2D MoS2 (~400 cm2 V-1 s-1), and being comparable to those for InSe (103 cm2 V-1 s-1) and black phosphorene (103-104 cm2 V-1 s-1). It is strong suggested that the (0 0 2) orientated PbPdO2 slab with high mobility should be an ideal candidate material for the application of electronics devices.