In this talk, we discuss some geometric and combinatorial propositions of planar graph with nonnegative combinatorial curvature, including the total curvature of planar graphs, the sharp upper bound for the number of vertices with positive curvature in a planar graph with nonnegative combinatorial curvature and the 4-regular planar graphs with nonnegative curvature. This is based on joint work with Bobo Hua, Lili Wang et al.