Composites of boron nitride (BN) and carboxylated graphene are prepared for the first time using covalent cross-linking employing the carbodiimide reaction. The BN(1-x)G(x) (x approximate to 0.25, 0.5, and 0.75) obtained are characterized using a variety of spectroscopic techniques and thermogravimetric analysis. The composites show composition-dependent electrical resistivity, the resistivity decreasing with increase in graphene content. The composites exhibit microporosity and the x approximate to 0.75 composite especially exhibits satisfactory performance with high stability as an electrode in supercapacitors. The x approximate to 0.75 composite is also found to be a good electrocatalyst for the oxygen reduction reaction in fuel cells.