In a traditional sense, Dammann grating can transfer the beam into one dimensional spots or two dimensional spots, which can be used for beam splitter or array illuminators. This paper presents a new kind Dammann grating that can realize the equal peak value intensity circular diffractive field. We call it circular Dammann grating. And the order of the grating is the number of the circular diffractive spectrums. We use the binary phase-only mask in our numerical simulation, we have obtained the optimized parameters, including the circular phase and radius of each ring. Our optimization algorithm is the simulated annealling algorithm. Different order circular Dammann grating can generate different circular diffractive field. We have calculated the number from 1 to 9 diffractive spectrums and found that with the increase of the encoding number of circular Danimann grating, more circular equal-intensity diffractive spectrums can be realized. Different order Dammann gratings have practical applications for different purposes. For example, the first order circular Dammann grating produce the smooth intensity in the central lobe, which can be used as the flat-top intensity for the wide applications of optical interference, such as producing optical fiber grating, optical detection, etc. The multi order Dammann grating can be used for beaming shaping and laser demonstration. In conclusion, circular Dammann grating is a novel diffractive optical element that has wide applications in optical information system.