The frequency tunable amplitude squeezed light of the continuous tunable range over 1 GHz around the D 2 line of Cesium (Cs) at 852.356 nm and the squeezing degree about 0.8 dB was experimentally generated with an injection locked laser diode. The amplitude squeezed light was applied in the frequency modulation (FM) spectroscopy measurement of Cs saturated vapor, the signal to noise ratio (SNR) of which was improved about 0.7 dB relative to the shot noise limit (SNL).