We study a class of gossip networks where a single source delivers fresh status updates through networks consisting of a set of gossiping nodes. Contrary to previous works, the source delivers the updates to the nodes subject to an age-dependent point process where the update rates are related to the polynomials of the age process on each node. We derive the closed-form expressions of stationary age moments for the disconnected networks, and demonstrate the general procedure for the moment analysis in the age-dependent gossip networks based on stochastic hybrid systems (SHSs). Considering the analytic difficulties in solving the infinite-dimensional moment dynamic equations in more complex topologies, we provide numerical methods to solve for the numerical values of stationary age moments approximately, and verify the effectiveness of these two methods on the first three age moments in ring networks.