A new time-domain theory for waveguides has been presented in the paper. The electromagnetic fields are first expanded by using the complete sets of vector modal functions derived from the transverse electric field. The expansion coefficients are then determined by solving inhomogeneous Klein-Gordon equation in terms of retarded Green's function. The theory has been validated by considering propagation problems excited by various excitation waveforms, which indicates that the higher order modes play a significant role in the field distributions excited by a wideband signal.