Abstract: Aimed to obtain small-sized beam spots, the focusing characteristics of high current electron beams generated by linear induction accelerators (LIA) with the quadrupole magnets were studied in this paper. The main factors which influence the minimum beam spot size of high current electron beams were analyzed. The high-order magnetic field components and nonlinear effects between a quadrupole magnet and a solenoid coil were compared, and the expressions for the minimum beam spot radius when focusing with quadrupole magnets were derived. Based on this, it is pointed out that under the same incident electron beam parameters, it is a potential to use a quadrupole magnet with stronger focusing ability and smaller aberration as a focusing element in order to achieve better focusing of high current electron beams and obtain smaller beam spot sizes. Then the key designing points for the focusing beam line of a quadrupole magnet were proposed. The quadrupole magnet focusing beam lines were simulated with Trace-3D and BEAMPATH, and two types of focusing beam line designs and the expected minimum beam spot sizes were given. The first type is based on the existing quadrupole magnets while the second type is an optimized layout of stronger focusing quadrupole magnets. It can be seen from the numerical simulation results that the influence of electron beam energy divergence and emittance is smaller when the focused beam line is designed with a stronger focusing magnetic field, smaller beam transmission envelope and shorter focal length. An experimental study using the first type design was conducted on a linear induction accelerator to obtain small X-ray spots with an existing quadrupole magnet. The parameters such as electron beam energy and current intensity were measured for each shot, and the beam spot distribution at the bremsstrahlung target surface was equivalently obtained by measuring the X-ray spot distribution using a pin-hole imaging setup. In the experiment, when a focal length at the end is 245 mm the X-ray focal spots with good symmetry and half width less than 2 mm in both directions are obtained, which is similar to the numerical simulation results. At the same time, theoretical analysis and numerical simulation also gave an expectation to further achieve smaller focal spot sizes by using optimized design of quadrupole magnet focusing beam lines.