The paper introduces a novel method called Low-Rank Kernel Tensor Learning for Incomplete Multiple Views Clustering (LRKT-IMVC) to address the issue of incomplete multi-view clustering. LRKT-IMVC first introduces the concept of kernel tensor to explore inter-view correlations and then uses a low-rank kernel tensor constraint to capture consistency information for imputing missing kernel elements, thereby improving clustering quality. The method is designed to unify imputation and clustering into a single optimization process, incorporating low-rank kernel tensor constraints to capture more consistency information. An alternative optimization method is proposed to solve the resulting optimization problem, which is proven to converge. The effectiveness of LRKT-IMVC is demonstrated through experiments on seven well-known datasets with different missing ratios, showing superior performance compared to other recent methods. The main contributions of the paper include the introduction of the kernel tensor concept, the development of a versatile IMVC method with low-rank tensor constraints, and the comprehensive imputation of absent kernel elements using consistency information.The paper introduces a novel method called Low-Rank Kernel Tensor Learning for Incomplete Multiple Views Clustering (LRKT-IMVC) to address the issue of incomplete multi-view clustering. LRKT-IMVC first introduces the concept of kernel tensor to explore inter-view correlations and then uses a low-rank kernel tensor constraint to capture consistency information for imputing missing kernel elements, thereby improving clustering quality. The method is designed to unify imputation and clustering into a single optimization process, incorporating low-rank kernel tensor constraints to capture more consistency information. An alternative optimization method is proposed to solve the resulting optimization problem, which is proven to converge. The effectiveness of LRKT-IMVC is demonstrated through experiments on seven well-known datasets with different missing ratios, showing superior performance compared to other recent methods. The main contributions of the paper include the introduction of the kernel tensor concept, the development of a versatile IMVC method with low-rank tensor constraints, and the comprehensive imputation of absent kernel elements using consistency information.