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Multiplex network embedding is an effective technique to jointly learn the low-dimensional representations of nodes across network layers. However, the number of edges among layers may vary significantly. This data imbalance will lead to performance degradation especially on the sparse layer due to learning bias and the adverse effects of irrelevant or conflicting data in other layers. In this paper, a Layer Imbalance Aware Multiplex Network Embedding (LIAMNE) method is proposed where the edges in auxiliary layers are under-sampled based on the node similarity in the embedding space of the target layer to achieve balanced edge distribution and to minimize noisy relations that are less relevant to the target layer. Real-world datasets with different degrees of layer imbalance are used for experimentation. The results demonstrate that LIAMNE significantly outperforms several state-of-the-art multiplex network embedding methods in link prediction on the target layer. Meantime, the comprehensive representation of the entire multiplex network is not compromised by the sampling method as evaluated by its performance on the node classification task.