The transient analysis of electromagnetic problems is important in the designing of plasmonic devices. It is useful for clarifying physical phenomena with extremely short timescales, because transient response affects the device performance. A timedomain computational technique is proposed for the transient analysis of electromagnetic problems with nanostructures. Our method is based on boundary integral equations in the complex frequency domain and fast inverse Laplace transforms. The advantage of our method is that the objects can be modeled by surface structure, dispersive media can be easily considered, computational error analysis is simple, and the electromagnetic field at the desired observation time can be obtained.