A new integrated measuring system with eight force-balance accelerometers is proposed to obtain a direct measurement of six degree-of freedom (DOF) ground motions, including three rotational and three actual translational acceleration components without gyroscopes. In the proposed measuring system, the relationship between the output from eight force-balance accelerometer and the six DOF motion of the measuring system under an earthquake are described by differential equations. These equations are derived from the positions and directions of the eight force-balance accelerometers in the measuring system. The third-order Runge-Kutta algorithm is used to guarantee the accuracy of the numerical calculation. All the algorithms used to compute the six DOF components of the ground motion are implemented in a real-time in Digital Signal Processor (DSP). The distortion of the measured results caused by position and direction errors of the accelerometers in the measuring system are reduced by multiplying a compensation coefficient C to the output and subtracting static zero drift from the measured results, respectively.