Pat the tenderloin dry with paper towel then season with salt and pepper.
Combine the remaining spices in a small bowl.
Rub the Cajun spice mixture into the tenderloin on all sides then place on a plate.
Cover and refrigerate for at least 2 hours and up to 24 hours.
Remove the tenderloin from the refrigerator and heat the grill to medium-high.
Place the tenderloin on the grill and cook for 15 to 20 minutes, turning occasionally to char evenly, until it reaches an internal temperature of 145°F.
Remove the tenderloin to a cutting board and let rest for 5 minutes before slicing to serve.