Metasurfaces have the characteristics of ultra-thin volume, light weight, and planar structure, which can also effectively control the polarization state of electromagnetic waves. We propose single-layer all-dielectric quarter-wave plate (QWP) and half-wave plate (HWP) metasurfaces that work in the visible light region in transmission mode. The designed QWP can convert y-linearly polarized (YLP) light into left-handed circularly polarized light, whereas the HWP can convert YLP light into x-linearly polarized light. Moreover, the designed wave plates have a certain wide band working ability. When the incident angle is <30  deg for the QWP and <28  deg for the HWP, the polarization conversion performance shows strong robustness. The effects of fabrication tolerance, the height of elliptic-shaped pillar, and lattice constant on the polarization conversion performance are analyzed. In addition, the physical mechanism of polarization conversion is revealed by simulating the distribution of magnetic field and electric field inside unit structures. The results indicate that nanostructures of different sizes will excite different magnetic dipole resonance modes so as to realize the function of different polarization state conversions. It is believed that all-dielectric wave plate metasurfaces will become a good alternative for controlling the polarization state of electromagnetic waves.