A method for detecting a target nucleic acid sequence from a DNA or a mixture of nucleic acids using a target signal generating primer (TSG primer), which comprises the steps of: (a) hybridizing the target nucleic acid sequence with the TSG primer to generate and obtain a signal indicative of the presence of the target nucleic acid sequence; wherein the TSG primer comprises (i) a hybridizing nucleotide sequence complementary to the target nucleic acid sequence and (ii) a reporter molecule and a quencher molecule; wherein the TSG primer has no self-complementary sequence which is functional in forming a hairpin stem-loop structure in its entire length; wherein when the TSG primer is not hybridized with the target nucleic acid sequence, the reporter molecule and the quencher molecule are three-dimensionally adjacent to each other with no help of hairpin stem-loop structures to allow the quencher molecule to quench a signal from the reporter molecule, thereby generating no signal indicative of the presence of the target nucleic acid sequence; wherein when the TSG primer is hybridized with the target nucleic acid sequence, the reporter molecule and the quencher molecule are three-dimensionally separated to allow the quencher molecule to unquench the signal from the reporter molecule, thereby generating the signal indicative of the presence of the target nucleic acid sequence with the reporter molecule and the quencher molecule remaining attached to the TSG primer; wherein where the template-dependent nucleic acid polymerase having a 3' to 5' nuclease activity is used and the TSG primer comprises at least one mismatch nucleotide sequence at its 3'-end portion or 3'-end, the mismatch nucleotide sequence has no label; (b) contacting the resultant of step (a) to a template-dependent nucleic acid polymerase under primer extension conditions such that the 3'-extension reaction at the 3'-end of the TSG primer is induced; and (c) detecting the signal indicative of the presence of the target nucleic acid sequence, whereby the signal indicates the presence of the target nucleic acid sequence in the DNA or the mixture of nucleic acids. (a) hybridizing the target nucleic acid sequence with the TSG primer to generate and obtain a signal indicative of the presence of the target nucleic acid sequence; wherein the TSG primer comprises (i) a hybridizing nucleotide sequence complementary to the target nucleic acid sequence and (ii) a reporter molecule and a quencher molecule; wherein the TSG primer has no self-complementary sequence which is functional in forming a hairpin stem-loop structure in its entire length; wherein when the TSG primer is not hybridized with the target nucleic acid sequence, the reporter molecule and the quencher molecule are three-dimensionally adjacent to each other with no help of hairpin stem-loop structures to allow the quencher molecule to quench a signal from the reporter molecule, thereby generating no signal indicative of the presence of the target nucleic acid sequence; wherein when the TSG primer is hybridized with the target nucleic acid sequence, the reporter molecule and the quencher molecule are three-dimensionally separated to allow the quencher molecule to unquench the signal from the reporter molecule, thereby generating the signal indicative of the presence of the target nucleic acid sequence with the reporter molecule and the quencher molecule remaining attached to the TSG primer; wherein where the template-dependent nucleic acid polymerase having a 3' to 5' nuclease activity is used and the TSG primer comprises at least one mismatch nucleotide sequence at its 3'-end portion or 3'-end, the mismatch nucleotide sequence has no label; (b) contacting the resultant of step (a) to a template-dependent nucleic acid polymerase under primer extension conditions such that the 3'-extension reaction at the 3'-end of the TSG primer is induced; and (c) detecting the signal indicative of the presence of the target nucleic acid sequence, whereby the signal indicates the presence of the target nucleic acid sequence in the DNA or the mixture of nucleic acids.