The harmonic optical frequency chain is the only tool for measuring optical frequency till the advent of a femtosecond optical frequency comb (FOFC). However, its disadvantages are obvious, such as high cost, difficult construction, complex usage, and complicated maintenance. The emergence of femtosecond optical frequency combs (FOFCs) makes it possible to measure the absolute frequency of a laser, which greatly simplifies the quantity traceability of the absolute frequency value and comparison, and allows the length unit “m” to be directly traced back to the time unit “s”. The beat note (fb) between an FOFC and a test laser is one of the most important data in measuring absolute frequency of the test laser. In order to ensure the accuracy and reliability of the measurement, the signal-to-noise ratio (SNR) of fb should be above 30 dB at 300 kHz resolution bandwidth. Among the wavelength standards recommended to replicate “meter” (SI), iodine-stabilized 633 nm lasers and iodine-stabilized 532 nm lasers have been widely used. Compared with iodine-stabilized 633 nm lasers, iodine-stabilized 532 nm lasers have the advantages of high stability, high output power, no modulation and fiber coupled output. Therefore, it is of great importance to measure and monitor the absolute frequency of an iodine-stabilized 532 nm laser. Aiming at the specific requirements for absolute frequency measurement of an iodine-stabilized 532 nm laser, the absolute frequency measurement of its fundamental 1064 nm laser has been studied. In this paper, a high-repetition-rate Er-doped femtosecond fiber laser is adopted as an optical source in the system. The repetition rate of the fiber laser is 303 MHz, the output power in the continuous-wave state is 130 mW and the average output power in the mode-locking state is 80 mW. The highest SNR of fb between the comb light and a 1064 nm laser generated by an iodine-stabilized 532 nm laser is only 30 dB due to the low intensity at 1 μm wavelength in the supercontinuum, which just reaches the SNR threshold meeting the counter's working condition. In order to improve the accuracy and reliability of absolute frequency measurement, the technique of cascading an Yb-doped fiber amplifier after spectral broadening is adopted to enhance the spectral intensity at 1 μm wavelength. The experimental results indicate that the SNR of fb between a 1 μm laser after spectral enhancement and a 1064 nm laser is increased by 5 dB and kept at 35 dB for several days, meeting requirements for long-term continuous monitoring. This method can effectively reduce the intensity requirements at 1 μm wavelength when the spectrum is directly broadened in the Er-FOFC.