Extreme ultraviolet lithography (EUVL) is the next generation lithography for the semiconductor manufacturer to achieve 22 nm node and below. Design of the projection objective is a core technology for the high-resolution lithography. An optical projection system with six high-order aspheric mirrors is presented to meet the industrial needs of the extreme ultraviolet lithography at 22 nm node. In the catoptrics embodiment of the present design, an image numerical aperture of 0.3 and a field width of 1.5 mm are obtained resulting in a working resolution of 25 nm across the exposure field, while the depth of focus is greater than 75 nm and modulation transfer function (MTF) larger than 45% without any resolution enhancement technologies. The mean wave front error of 0.0228λ (RMS) is reached. And the distortions of all field points are below 1.6 nm, CD (critical dimension) error is smaller than 1.6% while it is partial coherently illuminated (partial coherent factor 0.5～0.8). The total length of the system is 1075 nm. Image working distance is above 30 mm. Combined with resolution enhancement technologies, such as off-axis illumination or phase-shift mask, a greater depth of focus for 22 nm resolution can be achieved within the photoresist to meet extreme ultraviolet lithography lens industry need with 22 nm nodes.