The positioning and orientation system consists of three-axis generating coils and three-axis sensor coils in quasi-static magnetic field. The three-axis generating coils are fixed orthogonally and excited by the alternating current (AC) signals with different frequencies. They create the magnetic field that is equivalent to that generated by three orthogonal magnetic dipoles. Using the amplitude and phase information of the sensing signals in the sensor coils, the position and orientation parameters of the sensor coils can be computed by using an appropriate algorithm. In this paper, a novel algorithm is proposed to determine the position of the sensor coil object by some equations directly, so that its position and orientation parameters can be calculated much easier and faster. Based on this method, a system with support circuitry is designed with some special signal acquisition and sampling methods. Especially, a signal extraction (function fitting) method is proposed to pick up the coupling AC signal magnitude of the sensor coils, which simplifies the hardware circuitry and improves the signal acquisition accuracy. The simulation and real experimental results show that the system works satisfactorily with good accuracy.