As an effective deep clustering method, improved deep embedding clustering can process large-scale high-dimensional data. However, the method only focuses on the global data and does not consider the local graph structure between data points. In this paper, a semi-supervised deep clustering algorithm with soft membership affinity is proposed to cluster high-dimensional datasets. The proposed algorithm is composed of three parts: the reconstruction loss is adopted to recover data and extract important features on latent space, the KL divergence between the soft assignment and the target distribution is utilized to make samples in each cluster distribute more densely, and the novel soft membership affinity, which is regarded as the semi-supervised information, is introduced to the IDEC model to constrain the relationship between data points and their neighbors, so as to further enhance the clustering performance. Experiments on datasets show that the algorithm is effective compared with other deep clustering algorithms.