The concepts and characteristics of fractals and fractal dimension are firstly introduced. And the computation method of fractal dimension of dynamical system from one variable time series X (t) is mainly discussed. The computation technique of FD can be separated into two steps: reconstruction of phase space R (p) from X(t) and computation of relation integral and dimension for approaching to FD.The FD of ENSO is calculated by SST data at some grid points in central and eastern equatorial Pacific during the period from 1951 to 1979. The results show that FD of ENSO is 4. 95. 7 and ENSO is therefore proved to be a complicated chaotic system according to which five or six independent variables are enough to describe. Finally FD of some weather and climatic attractors is given.