The exponential scaling of dataset volumes in contemporary deep learning imposes great computational and storage burdens across learning paradigms, which emphasizes the importance of intelligent dataset compression methods. Dataset distillation (DD) emerges as a promising solution for dataset size reduction. This study focuses on the distribution matching framework for DD, introducing a novel methodology that quantifies the inter-distribution difference between source and distilled datasets via optimal transport theory, where Wasserstein metric \(W_1\) serves as the discrepancy measurement. We implement this metric via the Kantorovich-Rubinstein(KR) dual \(\sup _{f\in \text {Lip}(\varOmega)}\mathbb {E}_{\mu _\mathcal {T}}[f] - \mathbb {E}_{\mu _\mathcal {S}}[f]\) . According to Universal Approximation Theorem, a single-hidden-layer multilayer perceptron(MLP) with non-polynomial activation function can approximate continuous functions with arbitrary precision, thus a single-hidden-layer MLP is selected to approximate the function f in the expression of KR dual while maintaining its Lipschitz continuity through a parameter truncation technique. Empirical evaluations demonstrate that our approach achieves performance comparable to the mainstream benchmarks. The empirical findings of this study validate the operational feasibility of employing Wasserstein distance and KR dual in DD problem. Related code is available at https://github.com/muyangli17/DD-with-KR-dual .