In this paper, detrended fluctuation analysis is used to calculate the Hurst exponent, the fractal dimensions and finally the climate predictability indices of monthly and seasonal time series of air temperature, surface pressure, precipitation, wind speed and relative humidity for Beijing meteorological stations, in which the meteorological data cover a period from 1951 to 2009 and the precipitation data own a series of 286 years (1724~2009). And we found that at the monthly scale, the predictability of precipitation and wind speed was not controlled by temperature and pressure. A strong negative correlation showed for precipitation VS. temperature and pressure, and the persistence trait of wind speed just depended absolutely on itself. At the seasonal scale, all three meteorological parameters existed negative persistence behavior with temperature and pressure in winter. In spring, the persistence behavior of precipitation is in step with that of temperature and pressure, and for wind speed and relative humidity, it got unconformable results.