We have improved the performance of a previously reported multilayer zone plate by reducing its outermost zone width, using the same multilayer materials (MoSi2 and Si) and fabrication technique. The focusing performance was evaluated at the BL24XU of SPring-8 using 20-keV X-rays. The line spread function (LSF) in the focal plane was measured using a dark-field knife-edge scan method, and the point spread function was obtained from the LSF through a tomographic reconstruction principle. The spatial resolution was estimated to be 30 nm, which is in relatively good agreement with the calculated diffraction-limited value of 25 nm, while the measured diffraction efficiency of the + 1st order was 24%.