Abstract: Based on the concept of attractors of nonlinear system, the phase space with higher dimension is reconstructed by using observed single meteorological time series and then the weather attractor is embedded in it. The dimension of weather attractor and the weather predictability can be estimated from the time evolution of initially close pieces of trajectories. Computation results used daily data sets of the general circulation index at 500 hPa in Asia and Beijing temperature in wintertime show the fractal dimensions of 3.8 and 5.4 for these two attractors, respectively; and for which predictability time scale of 6-14 days, while weather predictability time scale of 4-9 days resulted from the e-folding expansion of trajectories in phase space.