Aircraft recognition is an extremely important task in air defense. In the existing literature, there exist only a few works on this topic. As a result, there is an urgent need to tackle this problem. In this paper we propose a novel method for aircraft recognition by polarizing the aircraft, extracting the Fourier features along the angle direction, and computing the dual-tree complex wavelet transform (DTCWT) features along the radial direction. We normalize the aircraft so that it is translation and scale invariant. Rotation invariance is achieved by taking the spectrum of the Fourier coefficients. We choose all except the finest scale of DTCWT coefficients and low frequency Fourier coefficients to classify the unknown aircraft because they are more robust to noise. Experimental results demonstrate that our new method is better than the Fourier-wavelet descriptor for all testing cases for a combination of scaling factors and rotation angles and a combination of noise levels and rotation angles, respectively.