The HfO2-based memristors have been acknowledged as a highly potential candidate for nonvolatile memory and neuromorphic computing applications. However, the analog resistive switching behavior of the HfO2-based memristors still needs improvement. In this work, Cu/HfO2/Pd devices with different oxide layer thicknesses were prepared by the magnetron sputtering process. The resistance switching characteristics related to oxide layer thickness were explored, revealing significant differences in the forming, SET, and RESET characteristics depending on oxide thickness. The conduction mechanism of the Cu/HfO2/Pd memristors is mainly attributed to the space charge limited current (SCLC) model. Thinner devices tend to show a more abrupt SET behavior and larger SET voltage, while thicker devices exhibit more gradual SET behavior and a lower SET voltage. In addition, as the thickness of the oxide layer increases, the Cu/HfO2/Pd memristors transition from digital resistive switching to analog resistive switching. The formation and rupture of oxygen vacancy filaments are predominant in thicker device, and the shape of the conduction filaments has been proposed as responsible for the abrupt and gradual changes in resistive switching. This work demonstrates that the thickness of the oxide layer plays an important role in engineering digital logic and neuromorphic behavior in HfO2-based memristors.