Abstract: High numerical aperture(NA) projection objectives with freeform surfaces are demanded for extreme ultraviolet lithography(EUVL) with high resolution. The traditional aspherical EUVL lens design is difficult to meet the need of correcting aberrations under a large NA, which often causes obscuration and destroys the imaging contrast. A design method of a high NA EUVL objective with freeform surfaces and without obscurations was proposed. Lens-form parameters were used to determine the best position to insert freeform surface, which could effectively correct aberrations and increase NA of the system without affecting the imaging performance. A set of high NA EUVL projection objective(PO) with freeform surfaces was designed by this method. Compared with the initial aspherical objective, by adding four freeform surfaces, the objective NA was increased from 0.3 to 0.35 and wavefront error RMS was reduced from 1 nm to 0.6 nm, and there was no obscuration in the entire optical path. The design results indicate that the proposed method effectively improves the design efficiency of the freeform surfaces EUVL objective. In the case of no obscuration, the system not only increases the NA, but also reduces the wavefront error, which greatly improves the overall performance of the objective.