How neurons are connected in the brain to perform computation is a key issue in neuroscience. Recently, the development of calcium imaging and multi-electrode array techniques have greatly enhanced our ability to measure the firing activities of neuronal populations at single cell level. Meanwhile, the intracellular recording technique is able to measure subthreshold voltage dynamics of a neuron. Our work addresses the issue of how to combine these measurements to reveal the underlying network structure. We propose the spike-triggered regression (STR) method, which employs both the voltage trace and firing activity of the neuronal population to reconstruct the underlying synaptic connectivity. Our numerical study of the conductance-based integrate-and-fire neuronal network shows that only short data of 20 ~ 100 s is required for an accurate recovery of network topology as well as the corresponding coupling strength. Our method can yield an accurate reconstruction of a large neuronal network even in the case of dense connectivity and nearly synchronous dynamics, which many other network reconstruction methods cannot successfully handle. In addition, we point out that, for sparse networks, the STR method can infer coupling strength between each pair of neurons with high accuracy in the absence of the global information of all other neurons.