Quantum steering is a recently defined form of quantum correlation which lies at the heart of quantum mechanics. In contrast to other types of quantum correlations, quantum steering is inherently asymmetric, which implies that it could manifest in one direction but not in the opposite direction. This rather peculiar phenomenon, known as one-way steering, has been demonstrated in several experiments, but subtlety remains. In fact, all experiments were shown to be ambiguous until a very recent conclusive one, which, however, made crucial use of a high-dimensional embedding to get around assumptions. This leaves the question open of whether the one-way steering phenomenon can be reliably demonstrated in the genuine two-qubit system. Here, we report such an experimental demonstration of one-way steering for a family of two-qubit states. Our experimental setup and results thus resolve the subtlety caused by fidelity assumption in previous experiments without the need for higher dimensional embedding. Moreover, our work provides a universal method to characterize one-way steering phenomenon for generic two-qubit states.