Nucleic acid detection is widely used in disease diagnosis, food safety, environmental monitoring and many other research fields. The continuous development of rapid and sensitive new methods to detective nucleic acid is very important for practical application. In this study, we developed a rapid nucleic-acid detection method using polymerase chain reaction (PCR) combined with electrokinetic preconcentration based on ion concentration polarization (ICP). Using a Nafion film, the proposed ICP microfluidic chip is utilized to enrich the nucleic acid molecules amplified by PCR thermal cycles. To demonstrate the capability of the microfluidic device and the hybrid nucleic-acid detection method, we present an animal-derived component detection experiment for meat product identification applications. With the reduced cycle numbers of 24 cycles, the detection can be completed in about 35 min. The experimental results show that this work can provide a microfluidic device and straightforward method for rapid detection of nucleic acids with reduced cycle numbers.