Clustering has been widely conducted in the analysis of gene expression data. For complex diseases, it has played an important role in identifying unknown functions of genes, serving as the basis of other analysis, and others. A common limitation of most existing clustering approaches is to assume that genes are separated into disjoint clusters. As genes often have multiple functions and thus can belong to more than one functional cluster, the disjoint clustering results can be unsatisfactory. In addition, due to the small sample sizes of genetic profiling studies and other factors, there may not be sufficient evidence to confirm the specific functions of some genes and cluster them definitively into disjoint clusters. In this study, we develop an effective overlapping clustering approach, which takes account into the multiplicity of gene functions and lack of certainty in practical analysis. A penalized weighted normalized cut (PWNCut) criterion is proposed based on the NCut technique and an norm constraint. It outperforms multiple competitors in simulation. The analysis of the cancer genome atlas (TCGA) data on breast cancer and cervical cancer leads to biologically sensible findings which differ from those using the alternatives. To facilitate implementation, we develop the function pwncut in the R package NCutYX.