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The microbunching instability in the linear accelerator (linac) of a free-electron laser facility has always been a problem that degrades the electron beam quality. In this paper, a quite simple and inexpensive technique is proposed to smooth the electron beam current profile to suppress the instability. By directly adding a short undulator with a transverse gradient field right after the injector to couple the transverse spread into the longitudinal direction, additional density mixing in the electron beam is introduced to smooth the current profile, which results in the reduction of the gain of the microbunching instability. The magnitude of the density mixing can be easily controlled by varying the strength of the undulator magnetic field. Theoretical analysis and numerical simulations demonstrate the capability of the proposed technique in the accelerator of an x-ray free-electron laser.