The undamping differential vibration equation of a six-axis accelerometer was derived based on the Lagrange equation. The theory of matrix iteration was introduced to solve the inherent frequencies and corresponding mode shapes of the six-axis accelerometer, and the theory can also avoid solving high-order differential equation which will happen in the traditional theories. The steps of matrix iteration were described in detail. It was found that every element of the system inertial matrix and stiff matrix is the function of the structure parameters in the calculation. For expanding the measuring range of the accelerometer and increasing the basic frequency, the relationship figures between the basic frequency and the structure parameters of the accelerometer were plotted by means of programming, which supplies the theoretical basis for the structure parameter optimization design of a six-axis accelerometer.