Curved shapes are increasingly used in buildings recently, which not only enriches the appearance of buildings, but also provides new possibilities of improving building performance by shape design. However, existing research relating building performance with building shapes focuses mostly on regular shapes; the effects of curved shapes on building performance should be better addressed. This paper aims to implement design optimization for curved shapes and to explore the performance improvement that they can contribute. Specifically, the improvements in daylight efficiency of office buildings by optimized curved facades are investigated. A typical office building with a curved facade is parametrically modeled in Rhinoceros, simulated in daylight by DIVA, and optimized by Galapagos to maximize its area-weighted average UDI. 20 optimizations are conducted, with 3 levels of geometrical complexity, 3 locations and 4 orientations. The results prove that optimized curved facades can significantly improve the daylight efficiency of office buildings, with improvements in area-weighted average UDI as high as 0.4376. Larger improvements can be achieved by curved facades with higher geometrical complexity, while the growth trend slows as the complexity increases. The improvements are also influenced by locations and orientations. Moreover, optimization for the best daylight efficiency can be a feasible method for finding novel curved shapes for architecture design. It is also found that the mechanism of the improvements is that the optimized curved facades reduce the time of daylight oversupply, although the side effect is the occurrence of uneven daylight distribution.