In　the　sparse　vector　recovery　problem,　the　L{0}　-norm　can　be　approximated　by　a　convex　function　or　a　nonconvex　function　to　achieve　sparse　solutions.　In　the　low-rank　matrix　recovery　problem,　the　nonconvex　matrix　rank　can　be　replaced　by　a　convex　function　or　a　nonconvex　function　on　the　singular　value　of　matrix　to　achieve　low-rank　solutions.　Although　the　convex　relaxation　can　easily　lead　to　the　optimal　solution,　the　nonconvex　approximation　tends　to　yield　more　sparse　or　lower　rank　local　solutions.　As　a　natural　extension　of　vector　and　matrix　to　high　order　structure,　tensor　can　better　represent　the　essential　structure　of　data　for　modeling　the　high-dimensional　data.　In　this　paper,　we　study　the　low　tubal　rank　tensor　recovery　problem　by　nonconvex　optimization.　Instead　of　using　convex　tensor　nuclear　norm,　we　use　nonconvex　surrogate　functions　to　approximate　the　tensor　tubal　rank,　and　propose　a　tensor　based　iteratively　reweighted　nuclear　norm　solver.　We　further　provide　the　convergence　analysis　of　our　new　solver.　Sufficient　experiments　on　synthetic　data　and　real　images　verify　the　effectiveness　of　our　new　method.　©　2013　IEEE.