Abstract: The Grosse-Wulkenaar model is a non-integrable matrix model with quartic interaction.  It is the first renormalizable model in non-commutative quantum field theory and is closely related to the Kontsevich model for the study of the two dimensional quantum gravity.  In this talk I will present some results about the construction of the two-dimensional Grosse-Wulkenhaar model with renormalization group analysis.