Based on the aqua-planet experiments, the wavenumber-frequency characteristics of tropical waves and their influcing factors in SST distribution and the convective parameterization scheme are investigated using the spectral atmospheric general circulation model (SAMIL). Space-time spectral analysis is used to obtain the variance of convectively coupled tropical waves. In the Control experiment with maximum SST located at the equator the simulated tropical-wave behaviors are in agreement with those in observations and theoretical solutions. When the maximum SST is located at 5°N, the symmetric and antisymmetric waves are much weaker than those in the control experiment, suggesting that tropical wave activities are very sensitive to the SST distributions. Importantly, the variance maximum of Madden-Julian oscillation (MJO) is found to occur around 5°N, which suggests that the development of the MJO depends largely on the latitude of maximum SST. Furthermore, the seasonal variations of MJO may be mainly caused by the seasonal variations of the maximum SST. The experiment results with two different cumulus schemes--the Manabe moist convective adjustment and Zhang-McFarlane (ZM) convective scheme, were also compared to examine the impacts of convective parameterization. Weakened variances of each individual tropical wave when the ZM scheme is used suggest that the ZM scheme is not favorable for the tropical wave activities. However, the wave characteristics are different when the ZM scheme is used in different models, which may imply that the simulated basic state is important to the meridional distributions of the waves. The MJO signals suggest that the parameterization scheme may have great influence on the strength, but have less direct impact on the MJO distribution. The frequency of the tropical waves may be associated with the moisture control of convection and the large-scale condensation scheme used in the model.