Abstract: In this paper, a tropical atmospheric model of relevance to short-term climate variations (Wang and Li 1993) is utilized for study of the development of Madden-Julian oscillation. The model contains an interactive process of boundy-layer Ekman convergence and precipitation heating. The model is solved by expanding dependent variables in terms of parabolic cylindrical functions in the meridional direction and truncating three meridional modes n=0, 2. 4 for equatorial symmetric solutions. The free wave solutions obtained under long-wave approximation are induced as a Kelvin wave and two Rossby waves. After considering the effect of boundary-laryer dynamic process, the modified Kelvin wave becomes unstable in long-wave bands with a typical growth rate on an order of 10-6 s-1 and an eastward phase speed of 10 ms-1;the most unstable mode is wavenumber one. These theoretical results are consistent with the observed Madden-Julian oscillation in equatorial area. For the two modified Rossby waves, one with a smaller meridional scale (n=4) decays except for extra long-waves;the other with a larger meridional sacale (n=2) grows in short-wave bands. This may be relevant to explaining the westward propagation of super cloud clusters in the Madden-Julian oscillation. The theory suggests that the boundary-layer dynamic process is an important mechanism in the development of the Madden-Julian oscillation.