The paper aims to reduce the lateral size of the X-ray source in a linear induction accelerator and design a bremsstrahlung conversion target. Analyzing the trajectory of the electron beam during the focused shooting process, it is pointed out that the distribution of the same electron beam trajectory can be described as either the transverse broadening of the electron beam at a certain longitudinal position or the axial distribution broadening when the electron beam maintains a small transverse size. Therefore, the concept design of a small-sized multi-layer target with multiple small targets placed near the waist to effectively block the focused electron beam is proposed. The EGS4 program was used to calculate the X-ray yield, and it was found that the change in X-ray yield was relatively small when the target thickness changed within a certain range. Based on this rule, the structural design of a small-sized multi-layer target was completed. Further investigation was conducted on a design application example. When the minimum envelope diameter of the focused electron beam is 3 mm and the convergence angle is 100 mrad, compared to large-sized targets, using a designed small-sized multi-layer target can obtain an X-ray light source with an equivalent diameter reduction of about 50% and a yield reduction of about 10%. By adopting the proposed design method, it is expected to obtain X-ray light sources with lateral dimensions smaller than the minimum envelope size of the electron beam under the same electron beam quality and focusing conditions, which has certain application value.