We present GeoSP, a parallel method that creates a parcellation of the cortical mesh based on a geodesic distance, in order to consider gyri and sulci topology. The method represents the mesh with a graph and performs a K-means clustering in parallel. It has two modes of use, by default, it performs the geodesic cortical parcellation based on the boundaries of the anatomical parcels provided by the Desikan-Killiany atlas. The other mode performs the complete parcellation of the cortex. Results for both modes and with different values for the total number of sub-parcels show homogeneous sub-parcels. Furthermore, the execution time is 82s for the whole cortex mode and 18s for the Desikan-Killiany atlas subdivision, for a parcellation into 350 sub-parcels. The proposed method will be available to the community to perform the evaluation of data-driven cortical parcellations. As an example, we compared GeoSP parcellation with Desikan-Killiany and Destrieux atlases in 50 subjects, obtaining more homogeneous parcels for GeoSP and minor differences in structural connectivity reproducibility across subjects.