The effects of pressure on the superconducting properties of a Bi-based layered superconductor La2O2Bi3Ag0.6Sn0.4S6, which possesses a four-layer-type conducting layer, have been studied through the electrical resistance and magnetic susceptibility measurements. The crystal structure under pressure was examined using synchrotron X-ray diffraction at SPring-8. In the low-pressure regime, bulk superconductivity with a transition temperature Tc of ~ 4.5 K was induced by pressure, which was achieved by in-plane chemical pressure effect owing to the compression of the tetragonal structure. In the high-pressure regime above 6.4 GPa, a structural symmetry lowering was observed, and superconducting transitions with a Tc ~ 8 K were observed. Our results suggest the possible commonality on the factor essential for Tc in Bi-based superconductors with two-layer-type and four-layer-type conducting layers.