A single-frequency low-noise green laser at 509 nm is developed for the study of cesium Rydberg atoms. The laser is generated by single-pass second-harmonic generation of a Yb fiber amplifier seeded with an external cavity diode laser (ECDL) at 1018 nm in a periodically poled MgO-doped lithium-niobate crystal. An up to 2.03 W, 509 nm laser is obtained from a 10.04 W incident 1018 nm laser with a conversion efficiency of 20.2%. The linewidth of the 509 nm laser is estimated to be 40 kHz according to the measured linewidth of 20 kHz of the 1018 nm fundamental laser. The relative intensity noise is 0.038% rms integrated from 10 Hz to 10 MHz.