Starting from the principle that the integer-period sampling (IPS) of periodic signals is free of spectrum leakage, in this paper we propose the multisine-IPS theory, deduce theoretically the sampling rate setting formula of multisine-IPS condition for the first time, and build its realization method based on field-programmable gate array (FPGA) plus digital-to-analog converter (DAC) plus analog-to-digital converter (ADC). A new multi-frequency electrical impedance tomography (mfEIT) system based on multisine excitation and its IPS theory is developed, and a dual-target imaging model including a carrot stick and a cucumber stick is designed. The experiments of multi-frequency time-difference imaging and frequency-difference imaging are carried out on the mfEIT system. The experimental results show that the newly-designed mfEIT system can achieve full-band impedance measurements on multiple objective tissue boundary at 20 frequency points (2–997 kHz) within one fundamental period (1 ms), and the structure and position of biological tissues with different electrical properties can also be distinguished from the resulting images. The proposed multisine-IPS theory and its implementation method can complete a full-band impedance measurement within one multisine fundamental period, which lays a theoretical and technical foundation for developing high-speed mfEIT system.