Abstract: Starting from a non-frictional and non-divergent nonlinear barotropic vorticity equation, using solution of the travelling waves, the linear and nonlinear bartropic instability criterions are gained respectively at an equilibrium point of the equation on a phase plane, these criterions are compared and analysed with the traditional instability criterions. The linear and nonlinear analysis solutions are also found. The computational results show that if amplitudes both of these instabilities are equal at initial time, the amplitude increments of the nonlinear barotropic instability are always less than these of the linear barotropic instability, the nonlinear effects can slow the exponential growing of linear instability, necessary time that two kinds of instabilities cause that amplitudes go up once as compar with initial ones for, is about 6 hours for linear instability, and is 18 hours for nonlinear instability, the latter is identical with the observational facts in the real atmosphere.