In this paper, we propose an optical frequency comb active filtering and amplification method combined with injection-locking technique to select and amplify a single mode from a femtosecond mode-locked laser. The key concept is to optically inject an optical frequency comb into a single mode grating external cavity semiconductor laser. The optical frequency comb based on a femtosecond mode-locked laser with a narrow mode spacing of 250 MHz is used as a master laser. The center wavelength of the optical frequency comb is 689 nm with a 10 nm spectral width. A single mode grating external cavity semiconductor laser with a grating of 1800 lines/mm is used as a slave laser, and the external-cavity length from the diode surface to the grating is approximately 50 mm. The master laser is injected into the slave laser, and in order to select a single comb mode, we adjust the power of the master laser to control the locking range of the slave laser whose linewidth is smaller than the optical frequency comb repetition rate (250 MHz). While the operating current of the slave laser is set to be 55 mA and a seeding power is adopted to be 240 W, a single longitudinal mode is selected and amplified from 2.5104 longitudinal modes of the femtosecond optical comb despite the low power of the single mode. By tuning the optical frequency comb repetition frequency, the single longitudinal mode follows the teeth of the femtosecond optical comb, indicating the success in the optical frequency comb active filtering and amplification. The locking range is measured to be about 20 MHz. Meanwhile, the repetition frequency of the optical frequency comb is locked to a narrow linewidth 698 nm laser system (Hz level), thus the slave laser inherits the spectral characteristics of the 698 nm laser system. The linewidth is measured to be 280 Hz which is limited by the test beating laser. Then a continuous-wave narrow linewidth 689 nm laser source with a power of 12 mW and a side-mode suppression ratio of 100 is achieved. This narrow linewidth laser is used as a second-stage cooling laser source in the 88Sr optical clock, the cold atoms with a temperature of 3 K and a number of 5106 are obtained. This method can also be used to obtain other laser sources for atomic optical clock, and thus enabling the integrating and miniaturizing of a clock system.