This　paper　addresses　solving　an　adaptive　l(1)-l(2)　regularized　model　in　the　framework　of　hierarchical　convex　optimization　for　sparse　signal　reconstruction.　This　is　realized　in　the　framework　of　bi-level　convex　optimization,　we　can　also　turn　the　challenging　bi-level　model　into　a　single-level　constrained　optimization　problem　through　some　priori　information.　The　l(1)-l(2　)norm　regularized　least-square　sparse　optimization　is　also　called　the　elastic　net　problem,　and　numerous　simulation　and　real-world　data　show　that　the　elastic　net　often　outperforms　the　Lasso.　However,　the　elastic　net　is　suitable　for　handling　Gaussian　noise　in　most　cases.　In　this　paper,　we　propose　an　adaptive　and　robust　model　for　reconstructing　sparse　signals,　say　l(p-)l(1)-l(2),　where　the　l(p)-norm　with　p　＞=　1　measures　the　data　fidelity　and　l(1)-l(2)-term　measures　the　sparsity.　This　model　is　robust　and　flexible　in　the　sense　of　having　the　ability　to　deal　with　different　types　of　noises.　To　solve　this　model,　we　employ　an　alternating　direction　method　of　multipliers　(ADMM)　based　on　introducing　one　or　a　pair　of　auxiliary　variables.　From　the　point　of　view　of　numerical　computation,　we　use　numerical　experiments　to　demonstrate　that　both　of　our　proposed　model　and　algorithms　outperform　the　Lasso　model　solved　by　ADMM　on　sparse　signal　reconstruction　problem.