Moment invariants have been a hot research topic for several decades already. Even though existing moment invariants are good for applications like pattern recognition, there is still a need to further improve the existing moment invariants published in the literature. In this paper, a new set of invariant moments is proposed by using the ridgelet function, which is good at capturing line features in a pattern image. It has been proven that this set of moments is invariant to the rotation of pattern images. Experimental results show that the proposed ridgelet moment invariants are better than the Fourier-wavelet descriptor and Zernike's moment invariants for pattern recognition under different rotation angles and different noise levels. It can be seen that the proposed ridgelet moment invariants can do an excellent job even when the noise levels are high.