In many real multi-view data, some views often lose some information, resulting in incomplete views. It is a challenging task to extract and fuse valuable information from the multi-view data with incomplete views for improving clustering performance. Incomplete multi-view clustering (IMC) is designed to fully mine patterns in data to reduce the negative impact of missing views. Many previous IMC methods are committed to discovers a consensus representation shared by all views. Nevertheless, this representation could severely deviate from the inherent representation of original data due to the loss of information caused by incomplete views. Besides, most existing spectral clustering-based multi-view subspace clustering independently performs similarity graph learning, Laplacian embedding, and discrete indicator matrix learning. This multi-step strategy might result in sharp performance degradation. In this paper, we propose a novel IMC method, referred to as Simultaneous Laplacian Embedding and Subspace Clustering (SLESC), to address the above issues. Specifically, in the paradigm for data self-representation, the proposed SLESC method learns a similarity graph for each view instead of learning a consensus graph for invoking traditional spectral clustering. Similarity graph learning, Laplacian embedding learning, weighting for each view, and discrete indicator matrix learning are seamlessly incorporated into the unified framework. The joint optimal clustering outcomes are therefore possible. Experimental results on real-world datasets in the IMC task demonstrate the effectiveness of the proposed method compared with state-of-the-art baselines.