Existing (multiple kernel learning, MKL) subspace clustering algorithms ignore the noise and the low-rank structure of the data in the feature space, therefore, we propose a new low-rank robust multiple kernel clustering algorithm (LRMKC) with block diagonal representation (BDR) and low-rank consensus kernel (LRCK), which is better for mining the underlying structure of the data. In particular, 1) to learn the optimal consensus kernel, we design an automatic weighting strategy using the mixture correntropy induced metric (MCIM), which not only sets the optimal weight for each kernel but also improves the robustness of the LRMKC by suppressing noise; 2) to explore the low-rank structure of input data in feature space, we learn the low-rank consensus kernel by the Schatten p-norm constraint on the optimal consensus kernel; 3) considering the block diagonal property of the affinity matrix, we apply block diagonal constraint to the coefficient matrix. The LRMKC combines MKL, LRCK, and BDR to solve these problems at the same time. Through the interaction of three technologies, the results of other technologies are used in the overall optimal solution to iteratively improve the efficiency of each technology, and finally form an overall optimal algorithm for processing nonlinear structural data. Compared with the most advanced MKL subspace clustering algorithms, extensive experiments on image and text datasets verify the competitiveness of the LRMKC.