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The large superconducting critical current (Ic) in superconductors is an important property for applications, but unfortunately, it is easily suppressed in the presence of a magnetic field. The stronger the magnetic field the lower the Icis the common response of superconductors. In this paper, we discovered a phenomenon that the Iccan be enhanced by a field-cooled process for the La0.67Sr0.33MnO3(LSMO)/YBa2Cu3O7−δ(YBCO)/La0.67Sr0.33MnO3(LSMO) trilayer system, in which the high-Tc-superconductor/oxide-ferromagnetic interface plays a crucial role. Three major factors based on a singlet superconducting picture, such as the difference in the work functions, the orbital hybridization, and the magnetic coupling between the induced Cu and Mn moments at the interface, decide the charge transfer and the capability of carrying maximum current. These factors can be preset by a field-cooling process with various field-cooled fields at a temperature higher than the superconducting transition temperature, Tc. While the system is field-cooled below Tc, we found that the competition between these factors and the responses of the interface may enhance or suppress the properties of the superconducting layer and finally gives rise to a maximum Icat a specific field-cooled field. Moreover, we also observed that the Icincreases with the increase of the applied magnetic field for the sample with a thinner YBCO layer, which cannot be explained by these mechanisms based on singlet superconductivity and strongly implies the possible existence of triplet superconducting pairs at the interface and inside a ferromagnetic (FM) layer.