In order to explore the stability of the flow, we study the nonlinear dynamical behavior and simulation problem of nine-modes Lorenz system for a two-dimensional incompressible Navier-Stokes equations. A new nine-modes truncation of Fourier series of Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is obtained. The symmetry, dissipation and existence of attractors of the system are studied, and the stationary solution and their stability properties are discussed. Based on numerical simulation results of bifurcation diagram, the Lyapunov exponent spectrum, Poincare section and power spectrum of the system, some basic dynamical behavior of the new system are investigated briefly, the physics process and evolution of the dynamical behavior from fixed point to periodic and chaotic behaviors are presented simultaneously.