The high-intensity noises of free-running lasers cannot meet the stringent requirements in the field of precision measurements such as gravitational wave detection. Taking ground-based gravitational wave detection project The Laser Interferometer Gravitational Wave Observatory (LIGO) as an example, its detection sensitivity was significantly improved after suppressing the laser intensity noises in the frequency range of 10 Hz to 10 kHz, which helps to directly observe the first gravitational wave signal in 2015. In order to obtain more information about the universe, researchers have attempted to expand the detection range of gravitational wave to the millihertz frequency range. So far, a few projects on space gravitational wave detection have been initiated around the world. Taking The Laser Interferometer Space Antenna (LISA) and Tianqin as examples, the space gravitational wave projects require laser sources to have their relative intensity noises below $\mathrm{2}\times {\mathrm{10}}^{-\mathrm{4}}\mathrm{H}{\mathrm{z}}^{-\mathrm{1}/\mathrm{2}}$ in the millihertz frequency range, $\mathrm{2}\times {\mathrm{10}}^{-\mathrm{6}}\mathrm{H}{\mathrm{z}}^{-\mathrm{1}/\mathrm{2}}$ in the 100 s kilohertz frequency range and $\mathrm{1}\times {\mathrm{10}}^{-\mathrm{8}}\mathrm{H}{\mathrm{z}}^{-\mathrm{1}/\mathrm{2}}$ in the megahertz frequency range. The seed lasers used in such projects are Non-Planar-Ring-Oscillators (NPRO) solid-state lasers, which have high intensity noises in the millihertz frequency range and high relaxation-oscillation noises in the 100 s kilohertz frequency range. Active noise suppression using feedback control loop must be applied on such lasers to meet the low-intensity noise requirements. The photodetector is one of the key components in active feedback control loop to convert optical signal to electrical signal with high efficiency and low noise. Motivated by the simultaneous suppression of millihertz intensity noise and 100 s kilohertz relaxation-oscillation noises in NPRO lasers, a wide-bandwidth and low-noise photodetector has been designed and tested in this work. The design strategies of this photodetector mainly include the following four points: firstly, select low-noise and high-response PIN-type InGaAs photodiodes to operate in photovoltaic mode to achieve low-noise measurement of weak signals; secondly, use low-noise zero-drift operational amplifiers to build integrators to reduce the contribution to total output noise at low frequencies from the high-speed operational amplifiers; thirdly, select low-noise high-speed operational amplifiers to meet the requirements of high-gain and high-bandwidth; fourthly, build a resistive capacitive network around the high-speed operational amplifier to enhance the cable driving capability. Configurations on the frequency response and noise level of the photodetector are theoretically calculated. Calculation results show that the detection bandwidth of the photodetector is approximate to 16 MHz; the noise level of the photodetector is lower than 1$\times {\mathrm{10}}^{-\mathrm{7}}\mathrm{V}/\mathrm{H}{\mathrm{z}}^{\mathrm{1}/\mathrm{2}}$ in 0.1 mHz to 1 Hz frequency range, and lower than 2$\times {\mathrm{10}}^{-\mathrm{8}}\mathrm{V}/\mathrm{H}{\mathrm{z}}^{\mathrm{1}/\mathrm{2}}$ in 100 kHz to 1 MHz frequency range. Experimental measurements show that the detection bandwidth of the photodetector is approximately 15 MHz; the noise level of the photodetector is lower than $\mathrm{1}\times {\mathrm{10}}^{-\mathrm{6}}\mathrm{V}/\mathrm{H}{\mathrm{z}}^{\mathrm{1}/\mathrm{2}}$ in 0.1 mHz to 1 Hz frequency range, and lower than $\mathrm{5}\times {\mathrm{10}}^{-\mathrm{8}}\mathrm{V}/\mathrm{H}{\mathrm{z}}^{\mathrm{1}/\mathrm{2}}$ in 100 kHz to 1 MHz frequency range. When the output voltage of the photodetector is larger than 1 V,the photodetector is possible to measure a laser with relative intensity noise lower than 1$\times {\mathrm{10}}^{-\mathrm{6}}\mathrm{H}{\mathrm{z}}^{-\mathrm{1}/\mathrm{2}}$ in the millihertz frequency range, and lower than $\mathrm{5}\times {\mathrm{10}}^{-\mathrm{8}}\mathrm{H}{\mathrm{z}}^{-\mathrm{1}/\mathrm{2}}$ in the 100 s kilohertz range. Therefore, this photodetector will provide a key support for achieving simultaneous suppression of millihertz intensity noises and relaxation-oscillation noises of NPRO lasers used for space gravitational wave detection or simultaneous suppression of multiband intensity noises of other similar lasers.