Quantum steering has been exploited as an important resource in modern quantum information processing. Owing to its directional nature, some quantum states that are asymmetric under the exchange of parties have been found to manifest steering only in a specific direction, thus called one-way steering. Existing works focused on one-way steering in systems of qubits. Here we propose a family of two-party states that are one-way steerable in systems of d dimensions. In particular, we validate the one-way steerability of the states for d=3, and demonstrate how one-way steering parameter space manifests in a two-qutrit system. A general numerical approach for characterizing higher-dimensional one-way steering is provided. Moreover, we develop a method to characterize one-way steering with the experimental loss taken into account, with which the trade-off relation between losses and measurement settings in a steering test in higher-dimensional system is investigated. Our loss-counted model works for finite-dimensional systems with finite measurement settings.