The recent report of pressure-induced structure transition and signature of superconductivity with T
c≈80 K above 14 GPa in the La3Ni2O7 crystals has garnered considerable attention. To further elaborate this discovery, we carried out comprehensive resistance measurements on the La3Ni2O7 crystals grown with the optical-image floating zone furnace under oxygen pressure (15 bar) by using the diamond anvil cell (DAC) and cubic anvil cell (CAC), which employs the solid (KBr) and liquid (Glycerol) pressure transmitting medium, respectively. For the sample #1 measured in DAC, it exhibits a semiconducting-like behavior with large resistance at low pressures and becomes metallic gradually upon compression. At the pressures P≥13.7 GPa, we observed the appearance of resistance drop as large as ~50% around 70 K, which evolves into a kink-like anomaly at pressures above 40 GPa and shifts to lower temperatures gradually with increasing magnetic field. These observations are consistent with the recent report mentioned above. On the other hand, the sample #2 measured in CAC retains the metallic behavior in the investigated pressure range up to 15 GPa. The hump-like anomaly in resistance around ~130 K at ambient pressure disappears at P≥2 GPa. In the pressure range from 11 GPa to 15 GPa, we observed the gradual development of a shoulder-like anomaly in resistance at low temperatures, which evolves into a pronounced drop of resistance by 98% below 62 K at 15 GPa, reaching a temperature-independent resistance of 20 μΩ below 20 K. Similarly, this resistance anomaly can be shifted to lower temperatures progressively by applying external magnetic fields, resembling a typical superconducting transition. Measurements on sample #3 in CAC reproduce the resistance drop at pressures above 10 GPa and realize the zero resistance below 10 K at 15 GPa even though an unusual semiconducting-like behavior retains in the normal state. Based on these results, we constructed a dome-shaped superconducting phase diagram and discussed some issues regarding the sample-dependent behaviors on the pressure-induced high-temperature superconductivity in the La3Ni2O7 crystals.