3D　object　detection　with　LiDAR　and　camera　fusion　has　always　been　a　challenge　for　autonomous　driving.　This　work　proposes　a　deep　neural　network　(namely　FuDNN)　for　LiDAR-camera　fusion　3D　object　detection.　Firstly,　a　2D　backbone　is　designed　to　extract　features　from　camera　images.　Secondly,　an　attention-based　fusion　sub-network　is　designed　to　fuse　the　features　extracted　by　the　2D　backbone　and　the　features　extracted　from　3D　LiDAR　point　clouds　by　PointNet++.　Besides,　the　FuDNN,　which　uses　the　RPN　and　the　refinement　work　of　PointRCNN　to　obtain　3D　box　predictions,　was　tested　on　the　public　KITTI　dataset.　Experiments　on　the　KITTI　validation　set　show　that　the　proposed　FuDNN　achieves　AP　values　of　92.48,　82.90,　and　80.51　at　easy,　moderate,　and　hard　difficulty　levels　for　car　detection.　The　proposed　FuDNN　improves　the　performance　of　LiDAR-camera　fusion　3D　object　detection　in　the　car　category　of　the　public　KITTI　dataset.