We report on the method of the sideband amplitude modulation (SAM) to achieve high-sensitivity spectroscopy with a fiber electro-optic modulator (fiber-EOM). This method increases the signal to noise ratio (SNR) by a factor of forty, comparing with conventional absorption spectroscopy. It is a temporal balanced detection to eliminate the intensity noise of the light source, and capable of preserving an undistorted Doppler profile for further quantitative analysis. Taking advantage of the newly developed fiber-EOM, SAM is applicable for various spectroscopies with a simple experimental setup. We performed SAM on CH43ν3 overtone band at 1170 nm using an external cavity Quantum dot laser. We demonstrated that one of the absorption lines buried in the other ten times stronger nearby lines was clearly extracted. SAM shows great potential on the molecular spectroscopy, where the spectrum is complicated and quantitative analysis is required.