Frequency-chirped free-electron lasers (FELs) are useful to generate a large photon bandwidth or a shorter xray pulse duration. In this paper, we present a threedimensional analysis of a high-gain FEL driven by the energy-chirped electron beam. We show that the FEL eigenmode equation is the same for a frequency-chirped FEL as for an undulator-tapered FEL. We study the transverse effects of such FELs including mode properties and transverse coherence.