In this letter, we propose a new conformal array architecture, called extremely large-scale uniform arc array (XL-UAA), to improve near-field communication performance. Specifically,under the non-uniform spherical wavefront channel model, we establish mathematical modeling and performance analysis for XL-UAAs. It is shown that XL-UAAs have larger direction-dependent Rayleigh distance and uniform power distance than the conventional XL uniform linear arrays (XL-ULAs). Moreover, a closed-form expression for the signal-to-noise ratio (SNR) is obtained, which depends on collective properties of XL-UAAs, such as the distance between the user and the array center,as well as the arc radius. In addition, we show that the asymptotic SNR of XL-UAAs with the number of antennas depends on the projection distance of the user to the middle of the arc array. Finally, numerical results verify that XL-UAAs achieve a higher SNR than XL-ULAs, especially at larger user incident angles.