Lov　&　aacute;sz　theta　SDP　problem　can　often　be　regarded　as　semidefinite　programming　(SDP)　relaxation　of　combinatorial　optimization　problems　in　graph　theory　and　appears　in　various　fields.　In　this　paper,　we　study　a　semismooth　Newton　based　augmented　Lagrangian　(Ssnal)　algorithm　for　solving　Lov　&　aacute;sz　theta　SDP　problem.　There　are　three　major　ingredients　in　this　paper.　Firstly,　we　design　efficient　implementations　of　the　Ssnal　algorithm　for　solving　dual　problem　of　Lov　&　aacute;sz　theta　SDP　problem.　Secondly,　the　global　convergence　and　local　asymptotic　superlinear　convergence　of　the　Ssnal　algorithm　are　characterized　under　very　mild　conditions,　in　which　a　semismooth　Newton　(Ssn)　method　with　superlinear　or　even　quadratic　convergence　is　applied　to　solve　the　subproblem.　Finally,　numerical　experiments　conducted　on　random　and　real　data　sets　demonstrate　that　the　Ssnal　algorithm　outperforms　Sdpnal+　solver.　In　particular,　the　Ssnal　algorithm　can　efficiently　solve　large-scale　Lov　&　aacute;sz　theta　SDP　problems　with　high　accuracy,　where　the　matrix　dimension　is　up　to　3000　and　the　number　of　equality　constraints　is　up　to　27,484.