We　theoretically　investigate　the　lift　forces　(including　shear　lift　and　rotational　lift)　experienced　by　nonspherical　convex　particles　rotating　in　a　linear　shear　flow　of　a　rarefied　gas,　based　on　the　gas　kinetic　theory.　In　our　model,　the　interactions　between　the　gas　molecules　and　the　particle　surface　are　assumed　to　be　the　Maxwell　combined　specular-diffuse　scattering.　By　integrating　the　general　expressions　for　several　simple　axisymmetric　bodies,　including　spheres,　cylinders,　disks,　and　spheroids,　the　specific　expressions　for　the　lift　forces　acting　on　these　bodies　are　obtained.　The　pitching　effect　of　the　nonspherical　particles　results　in　a　transverse　force　for　the　shear　lift,　but　there　is　no　transverse　force　for　the　rotational　lift.　The　expressions　for　the　orientation-averaged　shear　lift　forces　are　obtained　under　a　uniform　distribution　of　the　particle　orientation.　Published　by　AIP　Publishing.