The sheet electron beam with a quasi-rectangular cross section has been proposed to carry intense current. Obviously different from the elliptical sheet electron beam with the same high aspect ratio, this kind of beam is almost uniform in thickness, and can be generated by the cold metal cathode. Besides, the uniform thickness leads to uniform beam power in the horizontal direction, implying less modes but better counteraction between the beam and microwave. In addition, the uniform thickness make the width of the propagation system,including the cold cathode, the microwave cavities and the focusing magnets,easily changed. Firstly,the space-charge electric field of the sheet electron beam was analyzed numerically, then the focusing magnets, including the periodic cusped magnets and quadrupole magnets, were designed according to the space-charge electric field for beam matching. To validate the above theoretical analysis, particle-in-cell simulation was performed, which shows that the 300 keV, 3 kA sheet electron beam can be well focused by the 0.163 T periodic cusped magnetic fields with the 0.064 T quadrupole magnetic fields. More than 98% of the total current has been propagated through the distance of 300 mm.