Periodic Euler beam has flexural vibration band gap characteristics. In order to study the flexural vibration band gap features of the periodic Euler beam on the Winkler foundation, the transfer matrix method and Bloch theorem are used to calculate the vibration band structure and analyze the impact of the parameters of foundation and structure on the band gaps. The results show that the existence of Winkler foundation makes vibration band gaps trend to higher frequency, and a new band gap that starts at 0 Hz appears in the case of having a foundation. Additional results demonstrate that with increasing the foundation reaction modulus, the range of the 1st band gap becomes wider and the range of the 2nd band gap becomes narrower. Along with the increase of the length ratio, the range of the 1st band gap and the 2nd band gap both become narrower. Compared with the homogeneous Euler beam, periodic Euler beam has better vibration isolation characteristics at low frequency.