When the information of mutual coupling and shadowing effect of a conformal antenna array are unknown, the performance of direction of arrival (DOA) estimation will be seriously degraded by using some classical methods, such as the multiple signal classification (MUSIC) algorithm. Meanwhile it is difficult to measure or estimate the shadowing effect. The DOA estimation for a conformal uniform circular array (UCA) is studied. Firstly, the azimuthal angle is separated from all the unknown information by transforming the UCA from the element space to the mode space. Then the rank reduction (RARE) algorithm is applied in the estimation of the azimuthal angle. The π ambiguity existed in the RARE is solved by the beam forming. The main advantage of this method is that it does not need to measure the mutual coupling and the shadowing effect. Compared with the subarray method, it will not decrease the aperture of the array. Simulation results validate the advantages of the method.