A low-noise single-frequency laser is a key component of the space-based gravitational wave detector, and the intensity noise of the laser directly affects the sensitivity of the space-based GW detector. In this work, we report a low-noise single-frequency laser designed for space-based gravitational wave detector. The laser is based on a master oscillator power amplifier (MOPA), which is designed to possess a low-power, narrow-linewidth seed laser acting as master oscillator (MO) and an all polarization-maintaining fiber amplifier acting as power amplifier (PA). The amplifier that uses a robust mechanical design consists of an Yb-doped double-clad fiber forward pumped by wavelength-locked 976 nm pump laser diode (LD) to achieve 2.13 W of output power and 70 dB of signal-noise ratio (SNR). To suppress the relative intensity noise (RIN) in a millhertz regime (1 mHz–1 Hz), we characterize the power stabilization of a pump diode laser based on a proportional-integral-derivative (PID) feedback control loop where an in-loop photodetector is used. The power fluctuation can be converted into the fluctuation of the current signal by the photodiode, the current signal is converted into the voltage signal and amplified by a transimpedance circuit. Then, the voltage signal is compared with the voltage reference signal, and the error signal is achieved to adjust real-timely the drive current of the pump laser diode. This is a good way to significantly suppress the RIN of a laser at low frequencies, but the measured RIN below 4 mHz is still higher than –60 dBc/Hz. In order to further suppress the RIN to lower than 4 mHz, an active precise temperature control technology is used to suppress the thermal noise from pump LD and fiber coupler. To assess the RIN milliertz regime, we design an RIN measurement system consisting of a high-precision signal acquisition card (24 bit) and a computer program based on LabVIEW. The measurement range of the system is 2 μHz–102.4 kHz and the frequency resolution up to 2 µHz, much better than the counterparts of commercial instruments. By stabilizing the fiber amplifier pump LD current and the temperature of pump LD and the temperature of fiber coupler, the out-of-loop RINs are measured to be –63.4 dBc/Hz@1 mHz and –105.8 dBc/Hz@1 Hz , and in a milliertz regime of 1 mHz–1 Hz, the RIN is below –60 dBc/Hz. The results show that the feedback control of the fiber amplifier pump LD current and the temperature control of the key devices can effectively suppress the RIN in the millihertz frequency band, which lays a foundation for further improving the intensity noise performance in the low frequency band.