Micro-supercapacitors are important on-chip micro-power sources for miniaturized electronic devices. Although the performance of micro-supercapacitors has been significantly advanced by fabricating nanostructured materials, developing thin-film manufacture technologies and device architectures, their power or energy densities remain far from those of electrolytic capacitors or lithium thin-film batteries. Here we demonstrate graphene-based in-plane interdigital micro-supercapacitors on arbitrary substrates. The resulting micro-supercapacitors deliver an area capacitance of 80.7μFcm^-2 and a stack capacitance of 17.9Fcm^-3. Further, they show a power density of 495Wcm^-3 that is higher than electrolytic capacitors, and an energy density of 2.5mWhcm^-3 that is comparable to lithium thin-film batteries, in association with superior cycling stability. Such microdevices allow for operations at ultrahigh rate up to 1,000Vs^-1, three orders of magnitude higher than that of conventional supercapacitors. Micro-supercapacitors with an in-plane geometry have great promise for numerous miniaturized or flexible electronic applications.