Cyclic spectrum feature is one of the most popular features used in automatic modulation recognition (AMR) due to its excellent resiliency to noise. However, extracting cyclic features from wireless signals always requires at least Nyquist rate in traditional. What's more, to better capture cyclostationarity for modulation classification, the sampling rates typically used are higher than Nyquist rate. In this work, a novel AMR method based on compressive sensing principle is introduced, which is able to achieve good modulation recognition performance at sub-Nyquist rates. A new wavelet cyclic feature (WCF) is proposed to reduce the complexity of calculating classical cyclic spectrum. The relationship between nonuniform compressive samples and the WCF is established. A modified compressive sensing reconstruction algorithm is proposed to capture a small subset of magnitude peaks in WCF, which is sufficient for satisfactory modulation recognition. A hierarchical feature reduction method is employed for further reducing data dimension. Four digital modulation types, including BPSK, QPSK, MSK and 2FSK, are investigated and the simulation results show that the AMR with nonuniform compressive samples in sub-Nyquist rate outperforms the one based on classical Nyquist sampling rate.