The Serpens filament, a prominent elongated structure in a relatively nearby molecular cloud, is believed to be at an early evolutionary stage, so studying its physical and chemical properties can shed light on filament formation and early evolution. The main goal is to address the physical and chemical properties as well as dynamical state of the Serpens filament at a spatial resolution of ~0.07pc and a spectral resolution of ~0.1~km/s. We performed ^13^CO (1-0), C^18^O (1-0), C^17^O (1-0), ^13^CO (2-1), C^18^O (2-1), and C^17^O (2-1) imaging observations toward the Serpens filament with the IRAM-3 m and APEX telescopes. Widespread narrow ^13^CO (2-1) self-absorption is observed in this filament, causing the ^13^CO morphology to be different from the filamentary structure traced by C^18^O and C^17^O. Our excitation analysis suggests that the opacities of C^18^O transitions become higher than unity in most regions, and this analysis confirms the presence of widespread CO depletion. Further we show that the local velocity gradients have a tendency to be perpendicular to the filament's long axis in the outskirts and parallel to the large-scale magnetic field direction. The magnitudes of the local velocity gradients decrease toward the filament's crest. The observed velocity structure can be a result of gravity-driven accretion flows. The isochronic evolutionary track of the C^18^O freeze-out process indicates the filament is young with an age of <~2Myr. We propose that the Serpens filament is a newly-formed slightly-supercritical structure which appears to be actively accreting material from its ambient gas.