Femtosecond atomic-scale imaging is a most challenging subject in materials science and has long been a cherished dream tool for scientists wishing to study ultrafast structural dynamics. In this research, we aim to develop an innovative relativistic femtosecond-pulsed electron microscope by combining a radio-frequency (RF) acceleration-based electron gun technology into high-voltage electron microscope. In this paper, we reported the concept and construction of the relativistic femtosecond-pulsed electron microscope. Some demonstrations of electron microscopy imaging with 3.1-MeV femtosecond electron pulses were presented. The potential of RF gun for electron microscope was discussed.