In　this　letter,　a　constrained　visual　predictive　control　strategy　(C-VPC)　is　developed　for　a　robotic　flexible　endoscope　to　precisely　track　target　features　in　narrow　environments　while　adhering　to　visibility　and　joint　limit　constraints.　The　visibility　constraint,　crucial　for　keeping　the　target　feature　within　the　camera＇s　field　of　view,　is　explicitly　designed　using　zeroing　control　barrier　functions　to　uphold　the　forward　invariance　of　a　visible　set.　To　automate　the　robotic　endoscope,　kinematic　modeling　for　image-based　visual　servoing　is　conducted,　resulting　in　a　state-space　model　that　facilitates　the　prediction　of　the　future　evolution　of　the　endoscopic　state.　The　C-VPC　method　calculates　the　optimal　control　input　by　optimizing　the　model-based　predictions　of　the　future　state　under　visibility　and　joint　limit　constraints.　Both　simulation　and　experimental　results　demonstrate　the　effectiveness　of　the　proposed　method　in　achieving　autonomous　target　tracking　and　addressing　the　visibility　constraint　simultaneously.　The　proposed　method　achieved　a　reduction　of　12.3%　in　Mean　Absolute　Error　(MAE)　and　56.0%　in　variance　(VA)　compared　to　classic　IBVS.