An electrically-insulative threaded connection includes a pin member having a pin thread and a box member having a box thread. An insulating composite layer is disposed between the pin thread and the box thread. The insulating composite layer includes an insulating fiber and insulating resin. The pin thread and the box thread are wedge threads. A method of making an electrically-insulative threaded connection includes forming a pin wedge thread on a pin member and winding a filament over the pin wedge thread. The filament is wetted with a resin, thereby forming a composite layer. The composite layer is cured and machined to mate with a box wedge thread.