Energy-saving material such as soft magnetic ferrite has been widely adopted as the core material in power electronic devices. Due to the non-sinusoidal supply of power electronic devices, the core loss properties are quite complex so that it is more difficult to predict accurately under different supply waveforms. With the magnetic property measurement system for soft magnetic material, this study measures core losses of typical soft magnetic ferrite and nanocrystalline toroidal cores under the different supply waveforms, such as medium-frequency square, sinusoidal and PWM supplies. Further, in order to improve estimation accuracy of the Bertotti loss separation model under non-sinusoidal supply, the excess loss item is expressed by using the Barbisio algorithm, and the mathematical relationship between the excess loss and magnetizing frequency and strength is also proposed. Meanwhile, eddy current loss in the Bertotti model is derived further to fit for computing the eddy loss in the rectangular cross section of solid ferrite, and the proposed loss model is verified with the experimental data. Finally, the core loss of an intermediate frequency (IF) power electronics transformer is calculated under the square supply, the related experimental validation is also performed and the effectiveness of the proposed model are verified well. The achievement in this paper can provide the reference model for further optimization design and core performance analysis of electrical devices.