Fiber-reinforced polymer (FRP) composites have been widely employed to design advanced structural columns such as the hybrid FRP-concrete-steel double-skin tubular column (hybrid DSTC) with potential benefits. To date, the safety and self-monitoring of the hybrid DSTCs are still a challenge to overcome due to the complex damage scenarios. This paper investigates the self-sensing performance of a newly developed smart double-skin tubular confined concrete column (smart BFST-DSTC) made of basalt FRP-steel composite with built-in optical fiber Bragg grating sensors (OFBGs). The design of the smart BFST-DSTC and sensing principle are firstly addressed, followed by an experimental investigation on the basic mechanical properties and strain-based sensing performance of ten scaled specimens under axial compression. The outcomes reveal the enhancement of the proposed column in terms of load-carrying capacity, confinement ratio, and axial stress-axial strain behavior, as well as failure and damage modes when compared with the hybrid DSTC. The self-sensing investigation demonstrates that the measurement range satisfies the requirement to monitor and evaluate the hoop strains of the FRP jackets and the health state of the inner tube. The smart BFST-DSTC can replace the hybrid DSTC with the ability to provide early failure warning and life cycle health monitoring.