Cluster analysis is an important ingredient of unsupervised learning, and the classical clustering methods include K-means clustering, spectral clustering etc. These methods may get stuck in local optimal solutions due to the involved nonconvex optimization model. Recently, convex clustering has attracted a significant interest because its global optimal solution can be found easier than classical clustering methods. However, in high-dimensional scenarios, the performance of convex clustering is unsatisfactory because some noninformative features are included in the clustering. In this paper, considering the special structure of data, we propose a sparse group lasso convex clustering of high-dimensional data. And we prove that the proposed estimation has desirable statistical properties, including the finite sample bound for prediction error and feature screening consistency. Furthermore, we design a powerful semi-proximal alternating direction method of multipliers to solve the sparse group lasso convex clustering, and its convergence analysis is established without any conditions. Finally, the effectiveness of the proposed method is well demonstrated on synthetic and real datasets.