The　next-generation　wireless　network　is　expected　to　use　low-earth　orbit　(LEO)　satellite　networks　to　deliver　seamless　and　high-capacity　global　communications　services.　Due　to　the　high-speed　mobility　of　LEO　satellites,　massive　and　frequent　handovers　inevitably　occur.　Moreover,　handover　becomes　more　complicated　with　the　ever-growing　constellation　scale,　number　of　mobile　terminals　(MTs),　and　demands　for　emerging　delay-sensitive　applications.　In　this　paper,　a　decentralized　Markov　decision　process　(DEC-MDP)　is　adopted　to　formulate　the　handover　problem　in　the　LEO　satellite　network　with　finite　bursty　traffic.　The　target　is　maximizing　the　total　reward　associated　with　the　service　revenue　and　the　cost　of　handover　and　packet　loss.　To　deal　with　the　high　computational　complexity　caused　by　the　large　state　space　and　action　space,　the　solution　is　designed　using　a　multi-agent　double　deep　Q-network　(MADDQN)　with　fully　decentralized　framework,　which　also　allows　each　MT　to　train　and　use　an　individual　local　DDQN　to　avoid　load　imbalance　between　satellites.　Further,　to　alleviate　the　non-stationary　issue　of　the　environment　in　parallel　learning,　multi-agent　fingerprints　are　applied　in　MADDQN,　and　the　proposed　algorithm　is　called　multi-agent　fingerprints-enhanced　double　deep　Q-network-based　distributed　intelligent　handover　(MAF-DDQN-DIH)　mechanism.　The　implementation　of　MAF-DDQN-DIH　in　practical　communication　systems　are　discussed,　and　the　corresponding　communication　overhead　and　computational　complexity　are　analyzed.　Simulation　results　demonstrate　that　the　designed　multi-agent　fingerprints　are　effective　and　the　proposed　MAF-DDQN-DIH　algorithm　outperforms　the　comparison　handover　algorithms　in　terms　of　the　total　reward.