We have proposed a full dielectric (silicon) nanocube array polarizer based on a silicon dioxide substrate. Each polarization unit column includes a plurality of equal spaced polarization units. By optimizing the length, the width, the height of the polarization units and the center distance of adjacent polarization unit (x direction and y direction), an extinction ratio (ER) of higher than 25dB was obtained theoretically when the incident light wavelength is 1550nm. while for applications of most polarization optical elements, ER above 10dB is enough. With this condition, the polarizer we designed can work in a wide wavelength range from 1509.31nm to 1611.51nm. Compared with the previous polarizer, we have introduced a polarizer which is a full dielectric device, which solves the problems of low efficiency caused by Ohmic loss and weak coupling. Furthermore, compared with the existing optical polarizers, our polarizer has the advantages of thin thickness, small size, light weight, and low processing difficulty, which is in line with the future development trend of optical elements.