Feeling threaten and insecure?

My girlfriend and I have been together for 9 mths already. But there is a guy who keep on pestering her, keep showing lots of concern to her. He knows that we are together and yet he is doing it. And he also told my girlfriend to leave me and be with him. He told her how much he love her. My girlfriend didn't hide things from me, she told me certain things about him and what he did and told her before, but she don't wanna tell me more about him in more details, cos she said that she don't want me to worry and I might not be able to take it. I have told her that I really don't feel good about it and hope that she could make thing clear with him, I also want her to ignore him, she told me that she is ignoring him, but he keep going to her work place to see her, or even will go to her place to stalk at her. She sometime will tell me things like he did lots of amazing things for her, give her surprises and how nice he treated her, she feels touch for that, but she know she is with me and will not give him any chance. But she also said that sometime she feel confused as well. That make me very worry. I also love and treat my girlfriend very much, but due to my work, I don't have so much time to do those things that he did for my girlfriend. I wish I can have my own times or extra time to do things for her, but my work is really tough. He is a boss himself that why is can manage his own time. I trust my girlfriend and have faith in her, myself and our relationship, but I don't trust him as he tried to touch my girlfriend before, and turn aggressive before when she ignore him. I really worry and feel unsecure now.. Can anyone please advice me. I need help. Thanks.