Though constructing a model of delay-coupled modular neuronal network by Courbage-Nekorkin-Vdovin neuron elements, this paper numerically studies the effect of coupling strength and delay on the firing properties of burst synchronization. The results shows that appropriately large coupling strength can induce burst synchronization in this modular neuronal network. At the same time, it is found that coupling delay can induce the transitions of burst synchronization for the modular neuronal network. Moreover, all these transitions of burst synchronization occur approximately when the value of the delay approximately equates to the integer multiples of average oscillation period for all the neurons in the modular neuronal network. Additionally, delay-induced burst synchronization transitions are confirmed to be robust to the intra-coupling strength and the inter-connection probability in the modular neuronal network.