Synchronization behaviors of bursting neurons coupled through electrical and dynamic chemical synapses are investigated. The Izhikevich model is used with random and small world network of bursting neurons. Various currents which consist of diffusive electrical and time-delayed dynamic chemical synapses are used in the simulations to investigate the influences of synaptic currents and couplings on synchronization behavior of bursting neurons. The effects of parameters, such as time delay, inhibitory synaptic strengths, and decay time on synchronization behavior are investigated. It is observed that in random networks with no delay, bursting synchrony is established with the electrical synapse alone, single spiking synchrony is observed with hybrid coupling. In small world network with no delay, periodic bursting behavior with multiple spikes is observed when only chemical and only electrical synapse exist. Single-spike and multiple-spike bursting are established with hybrid couplings. A decrease in the synchronization measure is observed with zero time delay, as the decay time is increased in random network. For synaptic delays which are above active phase period, synchronization measure increases with an increase in synaptic strength and time delay in small world network. However, in random network, it increases with only an increase in synaptic strength.