Accurate travel time distribution prediction can comprehensively reflect the traffic conditions of each road segment of the freeway network in the future and assist in realizing fine management objectives such as route planning and accident warning on freeways. To this end, this study proposes a spatial-temporal neutral network with mixture density for freeway travel time distribution prediction. Specifically, adaptive graph convolution is used to extract the spatial features of the freeway network in a data-driven way, which effectively solves the problem that it is difficult to capture the complete spatial correlation of freeway network information based on predefined graphs. In the temporal dimension, a significant correlation exists in the freeway network at different times. Therefore, this study adaptively models the temporal correlation of freeway network information based on the attention mechanism and further aggregates the information between adjacent time steps through the convolution layer. Finally, according to the embedding of road segments obtained by adaptive spatio-temporal correlation modeling, the travel time distribution is modeled by a mixture density network to predict the travel time distribution in each road segment of freeways.