Abstract: In order to effectively model the strong bifurcation nonlinearity of magnetic resonance power amplifiers (MRPA), a time and power hybrid piecewise (TPHP) model is proposed in this paper. The TPHP model is an accurate nonlinear model for the MRPA with excitation of Sinc-pulse signal. The proposed model is segmented in time domain and amplitude domain based on the characteristics of the Sinc-pulse signal, so that the bifurcation nonlinearity of the MRPA can be accurately modeled. In order to demonstrate the merit of this nonlinear model, a 1.5 T (Frequency-63.89 MHz) MRPA with peak power 18 kW and Sinc-pulse signals are used in modeling, the duty cycle of test signal is 5%. The comparison between the measured AM/AM and AM/PM curves of the MRPA and the model shows that the TPHP model can accurately model the bifurcation nonlinearity of MRPA. At the same time, the proposed TPHP model leads to 10.7 dB, 10.3 dB and 14.7 dB improvement in the normalized mean square error (NMSE) compared with the traditional memory polynomial model, generalized memory polynomial (GMP) and time-division polynomial model for test signals.