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Abstract In this paper, we present a multi-frontal direct solver for one-dimensional iso-geometric finite element method. The solver implementation is based on the graph grammar (GG) model. The GG model allows us to express the entire solver algorithm, including generation of frontal matrices, merging, and elimi-nations as a set of basic undividable tasks called graph grammar productions. Having the solver algorithm expressed as GG productions, we can find the par-tial order of execution and create a dependency graph, allowing for scheduling of tasks into shared memory parallel machine. We focus on the implementation of the solver with NVIDIA CUDA on the graphic processing unit (GPU). The solver has been tested for linear, quadratic, cubic, and higher-order B-splines, resulting in logarithmic scalability. Keywords graph grammar, direct solver, isogeometric finite element method, NVIDI