Low noise continuous-wave single frequency 780 nm laser is generated high-efficiently by an extra-cavity-enhanced frequency doubler constructed from a periodically poled lithium niobate crystal and a linear cavity that is pumped by a continuous-wave single frequency fiber laser at 1.56 μm. Based on the design of the transmission of input coupler and the waist of cavity to optimize the mode and impedance matching of the frequency doubler, a second-harmonic laser at 780 nm is obtained experimentally with the output power of 1 W and conversion efficiency of 84.8%. Using a high fineness mode cleaner to reduce the laser intensity noise, a low noise 780 nm laser with the output power of 700 mW is achieved and intensity noise reaches the shot-noise-limit at analysis frequency of 4 MHz. The center wavelengths of the laser system at 1.56 μm and 780 nm are in the wave bands of quantum states transmission and quantum storage, respectively, so this kind of system can be employed for researches of practical quantum information processing.