This　paper　investigates　a　semismooth　Newton　based　augmented　Lagrangian　(SSNAL)　algorithm　for　solving　equivalent　formulation　of　the　general　l(1)　trend　filtering　problem.　The　computational　costs　of　a　semismooth　Newton　(SSN)　algorithm　for　solving　the　subproblem　in　the　SSNAL　algorithm　can　be　substantially　reduced　by　exploiting　the　second　order　sparsity　of　Hessian　matrix　and　some　efficient　techniques.　The　global　convergence　and　the　asymptotically　superlinear　local　convergence　of　the　SSNAL　algorithm　are　given　under　mild　conditions.　Numerical　comparisons　between　the　SSNAL　algorithm　and　other　state-of-the-art　algorithms　on　real　and　synthetic　data　sets　validate　that　our　algorithm　has　superior　performance　in　both　robustness　and　efficiency.