Aimed at the problems that the hyperbola positioning measure of adopting radio signal is limited by signal power or bandwidth, its positioning precision exists in hardly going beyond a ceiling and is susceptible to interference, insufficient measure distance and so on are becoming more obvious, the limitation of traditional radio signal system adopted by using quantum entanglement signals as measuring signals can greatly improve the precision and confidentiality. In this way, quantum positioning can be realized with advantages of ultraprecision, long range and strong antiinterference as well as noise resistance. According to that, a hyperbola positioning scheme based on twomode squeezed light and Bell state direct measurement is proposed. Twomode squeezed light is used as transmitting signals and in target receiving terminal Bell state direct measurement system is used to check two paths of entangled light and delay one of them. Then, the correlated noise of quadrature component is extracted and the delay time when the correlated noise value comes to the minimum can be seen as the moment of complete quantum correlation between two paths of light, which is the time difference of wave arrival between the two paths of entangled light. By measuring the time difference, the distance difference can be calculated to obtain a group of hyperbola. In this way, another two base points are chosen to repeat the process above to get the second hyperbola so as to conducting the positioning. By theoretical calculation and simulation analysis under some given conditions, the theoretical positioning precision and error range can be achieved.