Linear thermal expansion coefficient, which is vital for measuring the thermal expansion characteristics of metals, has been attracting considerable attention globally. Herein, a novel design based on Fresnel bimirror has been developed. In this design, when the upper end of the object to be measured comes in contact with a tilted double-sided mirror, the temperature rises and intersection angle of the Fresnel bimirror decreases. Meanwhile, interference fringe spacing becomes narrower, while the number of fringes increases. An imaging system based on a digital microscope and smartphone is also incorporated in this design, which records the changes in the interference fringes. Then, using a self-programmed software, the linear thermal expansion coefficients of Cu, Fe, and Al samples are determined at elevated temperatures as 17.85 +/- 0.23 x 10-6/degrees C (alpha Cu ${\alpha }_{C{\rm{u}}}$), 11.8 +/- 0.09 x 10-6/degrees C (alpha Fe ${\alpha }_{F{\rm{e}}}$), and 23.34 +/- 0.16 x 10-6/degrees C (alpha Al ${\alpha }_{Al}$), respectively, with a relative error of less than 1.6%. A cooling process is also designed, and the average value of the linear thermal expansion coefficient of metal samples during heating and cooling conditions is determined. The measurement results obtained via the finite-method simulation demonstrate the feasibility and reliability of the system. Overall, this study provides a new idea for measuring the linear thermal expansion coefficient of metals.