An adaptive filter for cancelling noise contained in the direct absorption spectra is reported. This technique takes advantage of the periodical nature of the repetitively scanned spectral signal, and requires no prior knowledge of the detailed properties of noises. An experimental system devised for measuring CH4 is used to test the performance of the filter. The measurement results show that the signal-to-noise (S/N) value is improved by a factor of 2. A higher enhancement factor of the S/N value of 5.4 is obtained through open-air measurement owing to higher distortions of the raw data. In addition, the response time of this filter, which characterizes the real-time detection ability of the system, is nine times shorter than that of a conventional signal averaging solution, under the condition that the filter order is 100.