Computational physics has been used in many scientific research fields, in which first-principles calculation based on density functional theory has made brilliant achievements. Unlike three-dimensional materials, low-dimensional materials present fantastic physical effect, due to the reduction of material dimensions. With the rapid development of two-dimensional materials, people have a more in-depth understanding of them. Requirements for high performance of two-dimensional materials are raised for potential applications, so the exploration of some effects affecting the stability of two-dimensional materials becomes more and more important. Based on the pioneers' work, Jahn-Teller effect is found to have a certain influence on the stabilities of two-dimensional structure of some elements. In the present paper, we explain the stable structure of Cr monolayer film through theoretical calculation, providing a guidance for experimental synthesis. Using first-principles calculation, we study a series of two-dimensional structures (rectangular, square, hexagonal, oblique and centered rectangular) of Cr monolayer film, focusing on the structural stability and electronic properties. Firstly, the equilibrium lattice constant and cohesive energy of each structure are calculated. Then, the bond angle and lattice constant dependence of the total energy are analyzed in detail. Finally, we investigate the energy band structures, total electronic densities of states, charge densities and electron occupation numbers of orbitals. The results show that low-symmetry oblique and centered rectangular lattice are stable in the two-dimensional system of Cr, while high-symmetry square and hexagonal lattices are not stable and the adhesive energy of the rectangular lattices is very small. Two stable structures of Cr monolayer sheet are formed due to hexagonal structure distortion. The hexagonal structure can shape into a centered rectangular structure with the increase of bond angle, while it changes into an oblique structure with the decrease of bond angle. Because of Jahn-Teller effect, the degenerate energy level spontaneously splits. Then the structure deforms into two reduced-symmetry structures, resulting in a stable system. Therefore, we can infer that the Jahn-Teller effect plays a crucial role in the structural stability of monolayer sheet.