According to the principle that light polarization can be expressed with a Stokes vector, a new system to measure the polarized skylight distribution is developed. The system is composed of a computer,a modified equatorial mount,an optical fiber spectrometer and an improved astronomical telescope mounted with a rotatable linear polarizer. The spectral resolution of this system is 1.4 nm for the measurement when wavelength ranges from 400 nm to 900 nm. Using modified equatorial mount, the system can scan the points of celestial hemisphere at azimuth ranges from 0°to 180° and elevation 0° to 90° at an angular resolution of 2.5°. For a full-angle viewing field of 4.5°, this system can measure the radiance intensity, the Degree of Linear Polarization (DOLP), and the Angle of Linear Polarization (AOLP) of the celestial. The calibration results show that the repeatability of intensity measurements is 99% in spectral ranges from 450 nm to 500 nm, and (95±3)% from 500 nm to 900 nm. The uncertainty of DOLP is less than 2% in spectral ranges from 400 nm to 750 nm, especially 1.2% at 475 nm.The angle error of AOLP is smaller than 2°.