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Recently, various studies have focused on the synchronization phenomenon in the nervous system. In this paper,we focused our attention on the underlying mechanism of synchronization and the robustness of synchronization through a simple unit network of globally coupled excitatory cells. Our network model with various numbers of neurons exhibits synchronized activities that originate from strong lateral excitatory connections. The degree of synchronization is quantified by the measure of the peak height of the power spectrum (PHPS). We find that the synchronization in the firing activities is a robust phenomenon against variations in the noise intensity even though the firing rate is sensitive to such variations. Our study on the robustness of synchronization can be a basis for a study on the role of synchronization in information processing.