The numerical solution of Boussinesq equations is worked out as an initial-value problem to study the effect of the instabilities of flow on the initial error growth and mesoscale predictability. The development of weather systems depends on different dynamic instability mechanisms according to the spatial scales of the system and the development of mesoscale systems is determined by symmetric instability. Since symmetric instability dominates among the three types of dynamic instability, it makes the prediction of the associated mesoscale systems more sensitive to initial uncertainties. This indicates that the stronger instability leads to faster initial error growth and thus limits the mesoscale predictability. Besides dynamic instability, the impact of thermodynamic instability is also explored. The evolvement of convective instability manifests as dramatic variation in small spatial scale and short temporal scale, and furthermore, it exhibits the upscale growth. Since these features determine the initial error growth, the mesoscale systems arising from convective instability are less predictable and the upscale error growth limits the predictability of larger scales. The latent heating is responsible for changing the stability of flow and subsequently influencing the error growth and the predictability.