The pressure-gradient driven flow in a three-dimensional cross-corrugated channel is investigated based on large eddy simulations. The channel geometry is highly tortuous so that the flow unsteadiness can be triggered at a moderate Reynolds number. The objective of this paper is to provide a better understanding of the laminar-to-chaotic transition in this type of channel. The transition from steady to chaos is found to occur at a low Reynolds number range between 77.4 and 113.1. The nonlinear dynamics is analyzed based on the power spectra of the velocity and reconstructed phase space. The route to chaos is identified, which favors the Ruelle-Takens-Newhouse scenario. Moreover, the transition from quasiperiodic mode to chaotic mode is accompanied with temporal intermittencies. The fluid dynamics is analyzed. It is found that the cross-corrugated geometry prompts a recirculating-and-rotating wake behind each contact corner. Each wake is enfolded by a pair of curved free shear layers. They are destabilized by the Kelvin-Helmholtz instability, leading to the periodic flow oscillation. Subsequently, the centrifugal instability sets in and promotes a type of primary vortex structures, forming streamwise “zig-zag” vortex streets. The competition between the adjacent vortex streets leads to a quasiperiodic flow. Temporal intermittencies emerge as the Reynolds number is increased. Finally, the periodicities in both the streamwise and spanwise directions are broken, and the flow becomes chaotic. When further increasing the Reynolds number to 343.1, Taylor-Görtler-like vortexes and necklace-like vortexes are formed in the channel.