Abstract: In this paper, an approuch for fast multiple sinusoidal frequency estimation is proposed which is based on the commonly used linear prediction (LP) method. In this approuch, we first reduce the order of the LP equation to half of its original value by taking into account the information that all the poles of the siunsoidal components lie on the unit circle of the Z-plane. The LP parameters can be recursively computed and the number of siunsoidal components in the signal can also be determined simultaneously. To extract signal frequencies, a high order polynomial equation must be solved. An elegent transformation of its roots is performed so that the problem of solving this high order complex-root polynomial equation is converted to a problem of solving a real -root polynomial equation with its order reduced by a half. The roots of this new polynomial euqation not noly lie on the real axis, but also distribute in a known finite interval. Based on this property, a fast convergent algorithm is presented for finding the roots of this new polynomial equation. Finally, computer simulation results are given, and comparison with LP and FBLP methods is also made.