Ion current rectification (ICR) in negatively charged conical nanopores is shown to be controlled by the electrolyte concentration gradient depending on the direction of ion diffusion. The degree of ICR is enhanced with the increasing forward concentration difference. An unusual rectification inversion is observed when the concentration gradient is reversely applied. A numerical simulation based on the coupled Poisson and Nernst-Planck (PNP) equations is proposed to solve the ion distribution and ionic flux in the charged and structurally asymmetric nanofluidic channel with diffusive ion flow. Simulation results qualitatively describe the diffusion-induced ICR behavior in conical nanopores suggested by the experimental data. The concentration-gradient-dependent ICR enhancement and inversion is attributed to the cooperation and competition between geometry-induced asymmetric ion transport and the diffusive ion flow. The present study improves our understanding of the ICR in asymmetric nanofluidic channels associated with the ion concentration difference and provides insight into the rectifying biological ion channels.