We present the detection of the shape-specific conformation of DNA based on the fluorescence resonance energy transfer (FRET) by using a novel flexible water-soluble cationic conjugated polymer (CCP). The flexible backbone of CCP has more conformational freedom with the potential to be responsive to analyte shape by electrostatic interaction between flexible CCP and negatively charged DNA. The analyte shape dependent recognition is accomplished by structural changes that compressed or extended the flexible CCP. The morphology-dependent spectral properties of the novel flexible polymer related to the analyte shapes are investigated in detail, where two types of chromophores, referred to as "isolated" segment and "packed" segment aggregates, within the flexible polymer are identified by means of ensemble and single molecule measurements upon binding with different geometric DNA. The change in fluorescence intensity upon binding with shape-specific DNA without obvious color shifts makes this novel flexible polymer a suitable CCP donor for FRET measurements. The results provide insights for understanding the spectral properties of flexible water-soluble CCP and CCP/DNA interaction related to the geometry of target analyte.