We propose a novel photonic technique for microwave frequency measurement based on transversal microwave filters with high resolution. Two parallel microwave filters with sine and cosine frequency responses are obtained by cross gain modulation in a single semiconductor optical amplifier, which introduces two different frequency responses to achieve an amplitude comparison function. We also demonstrate a proof-of-concept experiment. The measurement error is less than +-0.04 GHz for the first band range of 0-3.45 GHz and less than +-0.03 GHz for the second band range of 3.45-5.8 GHz. Our scheme is found to be capable of being extended for larger frequency range measurements using a shorter fiber length.