Superluminal lasers are lasers with a group velocity faster than the vacuum speed of light. Such a laser exhibits negative dispersion and thus an extremely sensitive relation between its lasing frequency and the length of its optical cavity. A gravitational wave detector can be constructed by using two superluminal lasers and measuring the beat frequency between them that results when an incident gravitational wave causes a change in the cavity length. A detector built in this way would be significantly smaller than existing detectors and potentially have a much higher sensitivity. We are investigating the behavior of superluminal lasers for this application and the necessary parameters to realize the construction of the detector.