P-texture effect on the fatigue crack propagation (FCP) resistance in an Al-Cu-Mg alloy containing a small amount of Ag, is investigated by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM) and electron back scattering diffraction (EBSD). Results shows that the high intensity P-texture sheet has lower ${\mathsf{\sigma }}_{0.2}/{\mathsf{\sigma }}_b$ , lower FCP rate and higher damage tolerance than random texture sheet. Fracture analysis indicates that the striations spacing of high intensity P-texture sheet is much smaller than that of random texture sheet and it has a rougher fatigue fracture surface, which causes a significant roughness induced crack closure (RICC) effect. The calculation results manifest that high intensity P-texture sheet possesses a higher crack closure level reaching 0.73 as compared to random texture sheet (only 0.25). The statistical analysis results reveal the P-grains have large twist angle of 105–170° and tilt angle of 5–60° with neighboring grains, which is similar to Goss-grains. This is the fundamental reason that P-texture sheet has the same FCP resistance and induces fatigue crack deflection as Goss-texture sheet. Additionally, the most {111} slipping planes of P-grains are distributed in the range of 30–50° deviating from transverse direction of the sheet. This results in more {111} slipping planes to participate in cyclic plastic deformation, which is beneficial to reduce fatigue damage accumulation and improve the damage tolerance of Al-Cu-Mg-Ag alloy.