We　demonstrated　MIR-pump　NIR-probe　photothermal　spectroscopy　with　the　first　harmonic　(PTS-1f)　detection　of　formaldehyde,　one　of　the　most　common　volatile　organic　compounds　(VOCs),　in　a　silica　hollow-core　negative　curvature　fiber　(HC-NCF).　The　photothermal　gas　sensor　adopts　a　mid-infrared　interband　cascade　pump　laser　at　3.6　mu　m　and　a　near-infrared　fiber　probe　laser　at　1.56　mu　m.　At　the　optimal　modulation　frequency　(8　kHz)　and　modulation　index　(1.8)　of　the　pump　laser,　we　obtained　a　normalized　noise　equivalent　absorption　(NNEA)　coefficient　of　4　x　10(-9)　cm(-1)WHz(-1/)2.　The　use　of　HC-NCF　with　an　inner　diameter　of　65　mu　m　enables　the　sensitive　photothermal　detection　even　for　a　very　low　pump　power　of　micro-watts.　The　background-free　PTS-1f　detection　was　observed　to　enhance　the　sensitivity　by　a　factor　of　2.4　compared　to　the　second　harmonic　(2f)　detection.　A　theoretical　model　was　established　in　this　work　to　interpret　the　experimental　results.