We focus on the role of heterogeneity on the propagation of firing patterns in feedforward network (FFN). Effects of heterogeneities both in parameters of neuronal excitability and synaptic delays are investigated systematically. Neuronal heterogeneity is found to modulate firing rates and spiking regularity by changing the excitability of the network. Synaptic delays are strongly related with desynchronized and synchronized firing patterns of the FFN, which indicate that synaptic delays may play a significant role in bridging rate coding and temporal coding. Furthermore, quasi-coherence resonance (quasi-CR) phenomenon is observed in the parameter domain of connection probability and delay-heterogeneity. All these phenomena above enable a detailed characterization of neuronal heterogeneity in FFN, which may play an indispensable role in reproducing the important properties of in vivo experiments.