We investigate the motion of overdamped Brownian particles in a one-dimensional channel under a zero-mean time-periodic tilting force F(t). By introducing a simple harmonic signal, strong enhancement of diffusion is possible for relatively large values of the Peclet number. Direct numerical simulations over the corresponding Fokker-Planck equation show that the diffusion enhancement is induced by a type of nonlinear resonance effect involving the tilting force and the density gradient.