A 633 nm laser interferometer has been designed based on a novel concept, which, without the acousto-optic modulator or the demodulator circuit, adopts the fibers to connect all elements except photodetectors and oscilloscope in this system to make it more compact, portable, and efficient. The noteworthy feature is to mathematically compare the two divided interference signals, which have the same phase-shift caused by the electron density but possess the different initial phase and low angular frequencies. It is possible to read the plasma density directly on the oscilloscope by our original mathematic demodulation method without a camera. Based on the Abel inversion algorithm, the radial electron density profiles versus time can be obtained by using the multi-chord system. The designed measurable phase shift ranges from 0 to 2π rad corresponding to the maximum line integral of electron density less than 3.5 × 10(17) cm(-2), and the phase accuracy is about 0.017 rad corresponding to the line integral of electron density accuracy of 1 × 10(15) cm(-2). After the construction of eight-chord interferometer, it will provide the detailed time resolved information of the spatial distribution of the electron density in the field-reversed configuration (FRC) plasma target produced by the "Yingguang-1" programmed-discharge device, which is being constructed in the Key Laboratory of Pulsed Power, China Academy of Engineering Physics.