Permeability anisotropy (A(p)) and gas slippage of shales are critical for shale gas exploration, but laboratory measurements are still limited. We investigated composition, pore structure, permeability anisotropy and gas slippage of the Longmaxi and Wufeng shales from the Sichuan Basin in South China. The total organic carbon (TOC) content is positively related with the effective porosity and volume fraction of micropores, suggesting enhanced pore connectivity by organic matter. Dependence of permeability on the effective pressure (i.e., the confining pressure minus the pore pressure of N-2) follows an exponential equation for five shale samples. At effective pressure of 6.9 MPa, our samples show very large A(p) variation from 1.2 to 1864.4. Compared with pore structure, clay content and the TOC content, microfractures significantly increase both permeability and Ap of shales and play a predominant role in shale gas production. For shales with A(p) > 4, A(p) generally decreases with the increasing effective pressure due to the closure of oriented microcracks and slit-shaped macropores. At effective pressure of 6.9 MPa, the gas slippage is observed in four cores, with deviation from the Klinkenberg plot in three cores at high pore pressure. A new equation is proposed to describe the log trend of measured permeability with pore pressure. It allows us to quantify the deviation amount from the Klinkenberg plot and to constrain the pore pressure range where the effective stress law breaks down. In addition, the deviation from the Klinkenberg plot is more significant in shales with relatively high permeability and large pore width. The dominant transport regime in shales can change from the slip flow to the Darcy flow in fracture bearing samples. The results indicate the important influence of permeability anisotropy and gas slippage of shales on final gas production and reservoir management.