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In this paper, we report on the active filtering and amplification of a single mode from an optical femtosecond laser comb with mode spacing of 250MHz by optical injection of two external-cavity diode lasers operating in cascade to build a narrow linewidth laser for laser cooling of the strontium atoms in an optical lattice clock. Despite the low injection of individual comb mode of approximately 50 nW, a single comb line at 689 nm could be filtered and amplified to reach as high as 10 mW with 37 dB side mode suppression and a linewidth of 240 Hz. This method could be applied over a broad spectral band to build narrow linewidth lasers for various applications. [ABSTRACT FROM AUTHOR]