Both simulations and observations have found that the spin of halo/galaxy is correlated with the large-scale environment, and particularly the spin of halo flips in filament. A consistent picture of halo spin evolution in different environments is still lacked. Using N-body simulation, we find that halo spin with its environment evolves continuously from sheet to cluster, and the flip of halo spin happens both in filament and nodes. The flip in filament can be explained by halo formation time and migrating time when its environment changes from sheet to filament. For low-mass haloes, they form first in sheets and migrate into filaments later, so their mass and spin growth inside filament are lower, and the original spin is still parallel to filament. For high-mass haloes, they migrate into filaments first, and most of their mass and spin growth are obtained in filaments, so the resulted spin is perpendicular to filament. Our results well explain the overall evolution of cosmic web in the cold dark matter model and can be tested using high-redshift data. The scenario can also be tested against alternative models of dark matter, such as warm/hot dark matter, where the structure formation will proceed in a different way.