The invention relates to a fluorescent high-molecular polymer and a preparation method of the fluorescent high-molecular polymer, in particular relates to a water-soluble cationic polyelectrolyte with an end group provided with fluorophore pyrene, a preparation method of the water-soluble cationic polyelectrolyte, and an application of water-soluble cationic polyelectrolyte in the detection of base sequences of nucleic acid molecules. A novel multi-stranded fluorescent probe is formed by electrostatic adsorption and hydrophobic interaction between the water-soluble cationic polyelectrolyte with the end group provided with fluorophore pyrene and single-stranded oligomerization nucleic acid molecules (DNAs with a hairpin structure and a linear chain structure). When nucleic acid molecules with base sequence structures complementary with those of the fluorescent probe exist, hybridization is performed through Watson-Crick base pairing principle, as the fluorescent pyrene at the end group is inserted into a DNA double-helix structure, the quenching ability of the base to the pyrene fluorescence is enhanced, so that the fluorescence intensity of the pyrene is remarkably reduced compared with that of the pyrene acted on non-target nucleic acid molecules, therefore, the specific identification of the base sequence structures of the nucleic acid molecules can be realized through difference of fluorescence properties of polyelectrolyte with fluorophore pyrene.