Focusing x-rays is a key technology for x-ray microscopic techniques. In a soft-x-ray region, focusing systems with achromaticity and a high numerical aperture have long been desired as a substitute for Fresnel zone plates. Ellipsoidal mirrors are promising focusing optics for such systems. However, two technical problems have to be overcome to allow practical application of these mirrors: their low efficiency due to their hollow shapes and strict requirements for their alignment. A novel focusing system using two reflective mirrors was proposed for this purpose. The downstream mirror is a quasi-Wolter mirror with a hollow shape similar to an ellipsoidal mirror and has a high numerical aperture of more than 0.1. The tolerance of the setting angle error of the quasi-Wolter mirror is significantly large compared to that of the ellipsoidal mirror because a quasi-Wolter mirror reflects the incident rays twice. The upstream mirror is a ring-focusing mirror, which produces an x-ray beam with a ring-shaped intensity profile, ensuring the entire beam reflects onto the quasi-Wolter mirror and reaches the focus of the system. The proposed system is ideal for soft-x-ray focusing. The design procedure and formulas are described in the present study. A prototype of the system is designed for BL25SU-A of SPring- 8. The ideal focusing spot size is estimated by numerical simulation to be 10 nm at 300 eV. The influence of alignment errors of the two mirrors is also simulated and summarized.