Quantum entanglement, quantum steering and Bell nonlocality, as significant quantum resources in the field of quantum information science, can achieve variously valuable quantum information tasks. Among of them, quantum entanglement and Bell nonlocality are the weakest and strongest nonlocal correlations, respectively. One can capture the quantum steering and Bell nonlocality via violating steering inequality and Bell inequality, respectively. In general, the detections of quantum steering and Bell nonlocality are strictly harder than entanglement detection. Here, based on steering inequality test and quantum state tomography, we attain various nonlocal correlations and experimentally demonstrate that the estimations of quantum steering and Bell nonlocality can be realized according to the quantum entanglement of the prepared two-photon test states. The estimated efficiency of quantum steering is stronger than the one of Bell nonlocality in this scenario, i.e., more steerable two-photon test states can be verified through quantum entanglement. In addition, quantum steering and Bell nonlocality are bounded by the corresponding upper and lower bounds, and these bounds cannot be punctured by all prepared two-photon states in experiment. These results are conducive to understand the relations among these nonlocal correlations.