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A theoretical analysis and calculation for the two-stream instability in a dual-sheet electron beam (DSEB) system immersed in an infinite magnetic field in semi-infinite space are proposed in this article. The dispersion equation of the DSEB system is obtained by solving the Maxwell equations. By analyzing the dispersion relation of two electron beams with different velocities, the instability generated by the coupling between the space charge waves is found, which leads to the growth of waves. Then, the growth rate of the instability is calculated. Furthermore, the impact of system parameters, such as the number density of electrons, the distance between two beams, and the thickness of beams, on the instability is analyzed. At last, a special case is discussed to further illustrate the mechanism of the instability. This study provides theoretical guidance for the utilization or avoidance of two-stream instability in the design and fabrication of dual-sheet beam vacuum electron devices (DSB-VEDs).