For simplicity's sake I would create a group. I would put the user in that group and then limit the visibility of the group only to the projects they are interested in.
Since you want to give access only to a project managed by the team, remove the group access to all projects and give access through the appropriate functionality in the administration section of the project itself.
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Your organization is probably using Roles to manage project access now. You can create a new User Group and apply it to only the project Permission Schemes where that User should have access.
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So, Once I will do this, All the other projects that I have should not be seen by that user in the list of projects, Correct?
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