Among existing mathematical models of electric energy measurement, either the full electric energy is calculated, or the fundamental active electric energy is conducted, or the fundamental and integer harmonic components of electric energy are separately determined. An electric energy measurement mathematical model that can fully take into account the influence of inter-harmonics is not yet well developed. In this paper, matrix pencil and singular value decomposition algorithm is used. After sampling the grid voltage and current signals, the matrix pencil algorithm is used to extract the characteristic frequency components, amplitudes, and initial phases. Then, the mathematical model of electric energy formed by the voltage and current of any two different frequency components is derived. The relevant electrical parameter information is substituted into the mathematical model, and the fundamental, harmonic, inter-harmonic and other electric energy components are obtained. The proposed algorithm is verified by numerical simulation tests. It is shown that in order to measure electric energy with high accuracy, the influence of inter-harmonics should be fully considered. The proposed new method of electric energy measurement has advantages over the FFT-based electric energy measurement algorithm.